Symmetry Problems The Navier Stokes Problem

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Symmetry Problems. The Navier–Stokes Problem.

Author : Alexander G. Ramm
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1681735067
Total Pages : 87 pages
Book Rating : 4.6/5 (817 download)

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Book Synopsis Symmetry Problems. The Navier–Stokes Problem. by : Alexander G. Ramm

Download or read book Symmetry Problems. The Navier–Stokes Problem. written by Alexander G. Ramm and published by Morgan & Claypool Publishers. This book was released on 2019-03-05 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It also gives necessary and sufficient conditions for a domain to be a ball if an overdetermined boundary problem for the Helmholtz equation in this domain is solvable. This includes a proof of Schiffer's conjecture, the solution to the Pompeiu problem, and other symmetry problems for partial differential equations. It goes on to study some other symmetry problems related to the potential theory. Among these is the problem of "invisible obstacles." In Chapter 5, it provides a solution to the Navier‒Stokes problem in R3. The author proves that this problem has a unique global solution if the data are smooth and decaying sufficiently fast. A new a priori estimate of the solution to the Navier‒Stokes problem is also included. Finally, it delivers a solution to inverse problem of the potential theory without the standard assumptions about star-shapeness of the homogeneous bodies.

Symmetry Problems

Author : Alexander G. Ramm
Publisher :
ISBN 13 : 9787576707465
Total Pages : 0 pages
Book Rating : 4.7/5 (74 download)

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Book Synopsis Symmetry Problems by : Alexander G. Ramm

Download or read book Symmetry Problems written by Alexander G. Ramm and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Symmetry Problems

Author : Alexander G. Ramm
Publisher : Springer Nature
ISBN 13 : 303102415X
Total Pages : 71 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Symmetry Problems by : Alexander G. Ramm

Download or read book Symmetry Problems written by Alexander G. Ramm and published by Springer Nature. This book was released on 2022-06-01 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It also gives necessary and sufficient conditions for a domain to be a ball if an overdetermined boundary problem for the Helmholtz equation in this domain is solvable. This includes a proof of Schiffer's conjecture, the solution to the Pompeiu problem, and other symmetry problems for partial differential equations. It goes on to study some other symmetry problems related to the potential theory. Among these is the problem of "invisible obstacles." In Chapter 5, it provides a solution to the Navier‒Stokes problem in ℝ³. The author proves that this problem has a unique global solution if the data are smooth and decaying sufficiently fast. A new a priori estimate of the solution to the Navier‒Stokes problem is also included. Finally, it delivers a solution to inverse problem of the potential theory without the standard assumptions about star-shapeness of the homogeneous bodies.

Initial-boundary Value Problems and the Navier-Stokes Equations

Author : Heinz-Otto Kreiss
Publisher : SIAM
ISBN 13 : 0898719135
Total Pages : 408 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Initial-boundary Value Problems and the Navier-Stokes Equations by : Heinz-Otto Kreiss

Download or read book Initial-boundary Value Problems and the Navier-Stokes Equations written by Heinz-Otto Kreiss and published by SIAM. This book was released on 1989-01-01 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation This book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. Researchers and graduate students in applied mathematics and engineering will find Initial-Boundary Value Problems and the Navier-Stokes Equations invaluable. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. There are many new results, in particular on the Navier-Stokes equations. The direct approach to the subject still gives a valuable introduction to an important area of applied analysis.

Introduction to Symmetry Analysis

Author : Brian J. Cantwell
Publisher : Cambridge University Press
ISBN 13 : 9781139431712
Total Pages : 670 pages
Book Rating : 4.4/5 (317 download)

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Book Synopsis Introduction to Symmetry Analysis by : Brian J. Cantwell

Download or read book Introduction to Symmetry Analysis written by Brian J. Cantwell and published by Cambridge University Press. This book was released on 2002-09-23 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry analysis based on Lie group theory is the most important method for solving nonlinear problems aside from numerical computation. The method can be used to find the symmetries of almost any system of differential equations and the knowledge of these symmetries can be used to reduce the complexity of physical problems governed by the equations. This is a broad, self-contained, introduction to the basics of symmetry analysis for first and second year graduate students in science, engineering and applied mathematics. Mathematica-based software for finding the Lie point symmetries and Lie-Bäcklund symmetries of differential equations is included on a CD along with more than forty sample notebooks illustrating applications ranging from simple, low order, ordinary differential equations to complex systems of partial differential equations. MathReader 4.0 is included to let the user read the sample notebooks and follow the procedure used to find symmetries.

The Navier–Stokes Problem

Author : Alexander G. Ramm
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1636391230
Total Pages : 79 pages
Book Rating : 4.6/5 (363 download)

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Book Synopsis The Navier–Stokes Problem by : Alexander G. Ramm

Download or read book The Navier–Stokes Problem written by Alexander G. Ramm and published by Morgan & Claypool Publishers. This book was released on 2021-04-06 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main result of this book is a proof of the contradictory nature of the Navier‒Stokes problem (NSP). It is proved that the NSP is physically wrong, and the solution to the NSP does not exist on ℝ+ (except for the case when the initial velocity and the exterior force are both equal to zero; in this case, the solution 𝑣(𝑥, 𝑡) to the NSP exists for all 𝑡 ≥ 0 and 𝑣(𝑥, 𝑡) = 0). It is shown that if the initial data 𝑣0(𝑥) ≢ 0, 𝑓(𝑥,𝑡) = 0 and the solution to the NSP exists for all 𝑡 ϵ ℝ+, then 𝑣0(𝑥) := 𝑣(𝑥, 0) = 0. This Paradox proves that the NSP is physically incorrect and mathematically unsolvable, in general. Uniqueness of the solution to the NSP in the space 𝑊21(ℝ3) × C(ℝ+) is proved, 𝑊21(ℝ3) is the Sobolev space, ℝ+ = [0, ∞). Theory of integral equations and inequalities with hyper-singular kernels is developed. The NSP is reduced to an integral inequality with a hyper-singular kernel.

The Navier-Stokes Equations

Author : Hermann Sohr
Publisher : Springer Science & Business Media
ISBN 13 : 3034805519
Total Pages : 376 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis The Navier-Stokes Equations by : Hermann Sohr

Download or read book The Navier-Stokes Equations written by Hermann Sohr and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary objective of this monograph is to develop an elementary and se- containedapproachtothemathematicaltheoryofaviscousincompressible?uid n in a domain ? of the Euclidean spaceR , described by the equations of Navier- Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers’ convenience, in the ?rst two chapters we collect, without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain ?. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n=2,3 that are also most signi?cant from the physical point of view. For mathematical generality, we will develop the l- earized theory for all n? 2. Although the functional-analytic approach developed here is, in principle, known to specialists, its systematic treatment is not available, and even the diverseaspectsavailablearespreadoutintheliterature.However,theliterature is very wide, and I did not even try to include a full list of related papers, also because this could be confusing for the student. In this regard, I would like to apologize for not quoting all the works that, directly or indirectly, have inspired this monograph.

The Navier–Stokes Problem

Author : Alexander G. Ramm
Publisher : Springer Nature
ISBN 13 : 3031024311
Total Pages : 61 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis The Navier–Stokes Problem by : Alexander G. Ramm

Download or read book The Navier–Stokes Problem written by Alexander G. Ramm and published by Springer Nature. This book was released on 2022-06-01 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main result of this book is a proof of the contradictory nature of the Navier‒Stokes problem (NSP). It is proved that the NSP is physically wrong, and the solution to the NSP does not exist on R+ (except for the case when the initial velocity and the exterior force are both equal to zero; in this case, the solution (, ) to the NSP exists for all ≥ 0 and (, ) = 0). It is shown that if the initial data 0() ≢ 0, (,) = 0 and the solution to the NSP exists for all ε R+, then 0() := (, 0) = 0. This Paradox proves that the NSP is physically incorrect and mathematically unsolvable, in general. Uniqueness of the solution to the NSP in the space 21(R3) × C(R+) is proved, 21(R3) is the Sobolev space, R+ = [0, ∞). Theory of integral equations and inequalities with hyper-singular kernels is developed. The NSP is reduced to an integral inequality with a hyper-singular kernel.

Symmetry And Perturbation Theory: Spt 98

Author : Antonio Degasperis
Publisher : World Scientific
ISBN 13 : 9814543160
Total Pages : 338 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Symmetry And Perturbation Theory: Spt 98 by : Antonio Degasperis

Download or read book Symmetry And Perturbation Theory: Spt 98 written by Antonio Degasperis and published by World Scientific. This book was released on 1999-12-30 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second workshop on “Symmetry and Perturbation Theory” served as a forum for discussing the relations between symmetry and perturbation theory, and this put in contact rather different communities. The extension of the rigorous results of perturbation theory established for ODE's to the case of nonlinear evolution PDE's was also discussed: here a number of results are known, particularly in connection with (perturbation of) integrable systems, but there is no general frame as solidly established as in the finite-dimensional case. In aiming at such an infinite-dimensional extension, for which standard analytical tools essential in the ODE case are not available, it is natural to look primarily at geometrical and topological methods, and first of all at those based on exploiting the symmetry properties of the systems under study (both the unperturbed and the perturbed ones); moreover, symmetry considerations are in several ways basic to our understanding of integrability, i.e. finally of the unperturbed systems on whose understanding the whole of perturbation theory has unavoidably to rely.This volume contains tutorial, regular and contributed papers. The tutorial papers give students and newcomers to the field a rapid introduction to some active themes of research and recent results in symmetry and perturbation theory.

Discrete Distributions in Engineering and the Applied Sciences

Author : Rajan Chattamvelli
Publisher : Springer Nature
ISBN 13 : 3031024257
Total Pages : 205 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Discrete Distributions in Engineering and the Applied Sciences by : Rajan Chattamvelli

Download or read book Discrete Distributions in Engineering and the Applied Sciences written by Rajan Chattamvelli and published by Springer Nature. This book was released on 2022-06-01 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory book on discrete statistical distributions and its applications. It discusses only those that are widely used in the applications of probability and statistics in everyday life. The purpose is to give a self-contained introduction to classical discrete distributions in statistics. Instead of compiling the important formulas (which are available in many other textbooks), we focus on important applications of each distribution in various applied fields like bioinformatics, genomics, ecology, electronics, epidemiology, management, reliability, etc., making this book an indispensable resource for researchers and practitioners in several scientific fields. Examples are drawn from different fields. An up-to-date reference appears at the end of the book. Chapter 1 introduces the basic concepts on random variables, and gives a simple method to find the mean deviation (MD) of discrete distributions. The Bernoulli and binomial distributions are discussed in detail in Chapter 2. A short chapter on discrete uniform distribution appears next. The next two chapters are on geometric and negative binomial distributions. Chapter 6 discusses the Poisson distribution in-depth, including applications in various fields. Chapter 7 is on hypergeometric distribution. As most textbooks in the market either do not discuss, or contain only brief description of the negative hypergeometric distribution, we have included an entire chapter on it. A short chapter on logarithmic series distribution follows it, in which a theorem to find the kth moment of logarithmic distribution using (k-1)th moment of zero-truncated geometric distribution is presented. The last chapter is on multinomial distribution and its applications. The primary users of this book are professionals and practitioners in various fields of engineering and the applied sciences. It will also be of use to graduate students in statistics, research scholars in science disciplines, and teachers of statistics, biostatistics, biotechnology, education, and psychology.

Fast Start Differential Calculus

Author : Daniel Ashlock
Publisher : Springer Nature
ISBN 13 : 3031024206
Total Pages : 222 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Fast Start Differential Calculus by : Daniel Ashlock

Download or read book Fast Start Differential Calculus written by Daniel Ashlock and published by Springer Nature. This book was released on 2022-06-01 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews the algebraic prerequisites of calculus, including solving equations, lines, quadratics, functions, logarithms, and trig functions. It introduces the derivative using the limit-based definition and covers the standard function library and the product, quotient, and chain rules. It explores the applications of the derivative to curve sketching and optimization and concludes with the formal definition of the limit, the squeeze theorem, and the mean value theorem.

Fast Start Integral Calculus

Author : Daniel Ashlock
Publisher : Springer Nature
ISBN 13 : 3031024214
Total Pages : 198 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Fast Start Integral Calculus by : Daniel Ashlock

Download or read book Fast Start Integral Calculus written by Daniel Ashlock and published by Springer Nature. This book was released on 2022-05-31 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces integrals, the fundamental theorem of calculus, initial value problems, and Riemann sums. It introduces properties of polynomials, including roots and multiplicity, and uses them as a framework for introducing additional calculus concepts including Newton's method, L'Hôpital's Rule, and Rolle's theorem. Both the differential and integral calculus of parametric, polar, and vector functions are introduced. The book concludes with a survey of methods of integration, including u-substitution, integration by parts, special trigonometric integrals, trigonometric substitution, and partial fractions.

Probability and Statistics for STEM

Author : E.N. Barron
Publisher : Springer Nature
ISBN 13 : 3031024273
Total Pages : 243 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Probability and Statistics for STEM by : E.N. Barron

Download or read book Probability and Statistics for STEM written by E.N. Barron and published by Springer Nature. This book was released on 2022-05-31 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most important subjects for all engineers and scientists is probability and statistics. This book presents the basics of the essential topics in probability and statistics from a rigorous standpoint. The basics of probability underlying all statistics is presented first and then we cover the essential topics in statistics, confidence intervals, hypothesis testing, and linear regression. This book is suitable for any engineer or scientist who is comfortable with calculus and is meant to be covered in a one-semester format.

An Introduction to Proofs with Set Theory

Author : Daniel Ashlock
Publisher : Springer Nature
ISBN 13 : 3031024265
Total Pages : 233 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis An Introduction to Proofs with Set Theory by : Daniel Ashlock

Download or read book An Introduction to Proofs with Set Theory written by Daniel Ashlock and published by Springer Nature. This book was released on 2022-06-01 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is intended as an introduction to mathematical proofs for students. It is distilled from the lecture notes for a course focused on set theory subject matter as a means of teaching proofs. Chapter 1 contains an introduction and provides a brief summary of some background material students may be unfamiliar with. Chapters 2 and 3 introduce the basics of logic for students not yet familiar with these topics. Included is material on Boolean logic, propositions and predicates, logical operations, truth tables, tautologies and contradictions, rules of inference and logical arguments. Chapter 4 introduces mathematical proofs, including proof conventions, direct proofs, proof-by-contradiction, and proof-by-contraposition. Chapter 5 introduces the basics of naive set theory, including Venn diagrams and operations on sets. Chapter 6 introduces mathematical induction and recurrence relations. Chapter 7 introduces set-theoretic functions and covers injective, surjective, and bijective functions, as well as permutations. Chapter 8 covers the fundamental properties of the integers including primes, unique factorization, and Euclid's algorithm. Chapter 9 is an introduction to combinatorics; topics included are combinatorial proofs, binomial and multinomial coefficients, the Inclusion-Exclusion principle, and counting the number of surjective functions between finite sets. Chapter 10 introduces relations and covers equivalence relations and partial orders. Chapter 11 covers number bases, number systems, and operations. Chapter 12 covers cardinality, including basic results on countable and uncountable infinities, and introduces cardinal numbers. Chapter 13 expands on partial orders and introduces ordinal numbers. Chapter 14 examines the paradoxes of naive set theory and introduces and discusses axiomatic set theory. This chapter also includes Cantor's Paradox, Russel's Paradox, a discussion of axiomatic theories, an exposition on Zermelo‒Fraenkel Set Theory with the Axiom of Choice, and a brief explanation of Gödel's Incompleteness Theorems.

Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations

Author : R. Glowinski
Publisher : SIAM
ISBN 13 : 9780898712780
Total Pages : 438 pages
Book Rating : 4.7/5 (127 download)

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Book Synopsis Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations by : R. Glowinski

Download or read book Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations written by R. Glowinski and published by SIAM. This book was released on 1991-01-01 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on the notion that by breaking the domain of the original problem into subdomains, such an approach can, if properly implemented, lead to a considerable speedup. The methods are particularly well suited for parallel computers.

The Navier-Stokes Problem

Author : Alexander G Ramm
Publisher :
ISBN 13 : 9781636391243
Total Pages : 77 pages
Book Rating : 4.3/5 (912 download)

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Book Synopsis The Navier-Stokes Problem by : Alexander G Ramm

Download or read book The Navier-Stokes Problem written by Alexander G Ramm and published by . This book was released on 2021-04-06 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main result of this book is a proof of the contradictory nature of the Navier‒Stokes problem (NSP). It is proved that the NSP is physically wrong, and the solution to the NSP does not exist on ℝ] (except for the case when the initial velocity and the exterior force are both equal to zero; in this case, the solution 𝑣(𝑥, 𝑡) to the NSP exists for all 𝑡 >= 0 and 𝑣(𝑥, 𝑡) = 0). It is shown that if the initial data 𝑣0(𝑥) ≢ 0, 𝑓(𝑥,𝑡) = 0 and the solution to the NSP exists for all 𝑡 ϵ ℝ+, then 𝑣0(𝑥): = 𝑣(𝑥, 0) = 0. This Paradox proves that the NSP is physically incorrect and mathematically unsolvable, in general. Uniqueness of the solution to the NSP in the space 𝑊21(ℝ3) × C(ℝ+) is proved, 𝑊21(ℝ3) is the Sobolev space, ℝ+ = [0, ∞). Theory of integral equations and inequalities with hyper-singular kernels is developed. The NSP is reduced to an integral inequality with a hyper-singular kernel.

Fundamental Trends in Fluid-structure Interaction

Author : Giovanni P. Galdi
Publisher : World Scientific
ISBN 13 : 9814299332
Total Pages : 302 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Fundamental Trends in Fluid-structure Interaction by : Giovanni P. Galdi

Download or read book Fundamental Trends in Fluid-structure Interaction written by Giovanni P. Galdi and published by World Scientific. This book was released on 2010 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interaction of a fluid with a solid body is a widespread phenomenon in nature, occurring at different scales and different applied disciplines. Interestingly enough, even though the mathematical theory of the motion of bodies in a liquid is one of the oldest and most classical problems in fluid mechanics, mathematicians have, only very recently, become interested in a systematic study of the basic problems related to fluid-structure interaction, from both analytical and numerical viewpoints. Fundamental Trends in Fluid-Structure Interaction is a unique collection of important papers written by world-renowned experts aimed at furnishing the highest level of development in several significant areas of fluid-structure interactions. The contributions cover several aspects of this discipline, from mathematical analysis, numerical simulation and modeling viewpoints, including motion of rigid and elastic bodies in a viscous liquid, particulate flow and hemodynamic.