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Author : James Serrin
Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.3/5 (91 download)
Download or read book On the Interior Regularity of Weak Solutions of the Navier-stokes Equations written by James Serrin and published by . This book was released on 1961 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hermann Sohr
Publisher : Springer Science & Business Media
ISBN 13 : 3034805519
Total Pages : 376 pages
Book Rating : 4.0/5 (348 download)
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.
Author : Hajer Bahouri
Publisher : Springer Science & Business Media
ISBN 13 : 3642168302
Total Pages : 530 pages
Book Rating : 4.6/5 (421 download)
Download or read book Fourier Analysis and Nonlinear Partial Differential Equations written by Hajer Bahouri and published by Springer Science & Business Media. This book was released on 2011-01-03 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. The present book aims at presenting self-contained, state- of- the- art models of those techniques with applications to different classes of partial differential equations: transport, heat, wave and Schrödinger equations. It also offers more sophisticated models originating from fluid mechanics (in particular the incompressible and compressible Navier-Stokes equations) or general relativity. It is either directed to anyone with a good undergraduate level of knowledge in analysis or useful for experts who are eager to know the benefit that one might gain from Fourier analysis when dealing with nonlinear partial differential equations.
Author : José F. Rodrigues
Publisher : Springer Science & Business Media
ISBN 13 : 3764373172
Total Pages : 290 pages
Book Rating : 4.7/5 (643 download)
Download or read book Trends in Partial Differential Equations of Mathematical Physics written by José F. Rodrigues and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of contributions originating from a conference in Obedo, Portugal, which honoured the 70th birthday of V.A. Solonnikov. A broad variety of topics centering on nonlinear problems is presented, particularly Navier-Stokes equations, viscosity problems, diffusion-absorption equations, free boundaries, and Euler equations.
Author : Jiri Neustupa
Publisher : Springer Science & Business Media
ISBN 13 : 9783764365936
Total Pages : 288 pages
Book Rating : 4.3/5 (659 download)
Download or read book Mathematical Fluid Mechanics written by Jiri Neustupa and published by Springer Science & Business Media. This book was released on 2001-08-01 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical modeling and numerical simulation in fluid mechanics are topics of great importance both in theory and technical applications. The present book attempts to describe the current status in various areas of research. The 10 chapters, mostly survey articles, are written by internationally renowned specialists and offer a range of approaches to and views of the essential questions and problems. In particular, the theories of incompressible and compressible Navier-Stokes equations are considered, as well as stability theory and numerical methods in fluid mechanics. Although the book is primarily written for researchers in the field, it will also serve as a valuable source of information to graduate students.
Author : Tomáš Bodnár
Publisher : Springer Nature
ISBN 13 : 3030396398
Total Pages : 647 pages
Book Rating : 4.0/5 (33 download)
Download or read book Fluids Under Pressure written by Tomáš Bodnár and published by Springer Nature. This book was released on 2020-04-30 with total page 647 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume is based on talks given at the August 2016 summer school “Fluids Under Pressure,” held in Prague as part of the “Prague-Sum” series. Written by experts in their respective fields, chapters explore the complex role that pressure plays in physics, mathematical modeling, and fluid flow analysis. Specific topics covered include: Oceanic and atmospheric dynamics Incompressible flows Viscous compressible flows Well-posedness of the Navier-Stokes equations Weak solutions to the Navier-Stokes equations Fluids Under Pressure will be a valuable resource for graduate students and researchers studying fluid flow dynamics.
Author : Giovanni P. Galdi
Publisher : Birkhäuser
ISBN 13 : 3034884249
Total Pages : 300 pages
Book Rating : 4.0/5 (348 download)
Download or read book Fundamental Directions in Mathematical Fluid Mechanics written by Giovanni P. Galdi and published by Birkhäuser. This book was released on 2012-12-06 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of six articles, each treating an important topic in the theory ofthe Navier-Stokes equations, at the research level. Some of the articles are mainly expository, putting together, in a unified setting, the results of recent research papers and conference lectures. Several other articles are devoted mainly to new results, but present them within a wider context and with a fuller exposition than is usual for journals. The plan to publish these articles as a book began with the lecture notes for the short courses of G.P. Galdi and R. Rannacher, given at the beginning of the International Workshop on Theoretical and Numerical Fluid Dynamics, held in Vancouver, Canada, July 27 to August 2, 1996. A renewed energy for this project came with the founding of the Journal of Mathematical Fluid Mechanics, by G.P. Galdi, J. Heywood, and R. Rannacher, in 1998. At that time it was decided that this volume should be published in association with the journal, and expanded to include articles by J. Heywood and W. Nagata, J. Heywood and M. Padula, and P. Gervasio, A. Quarteroni and F. Saleri. The original lecture notes were also revised and updated.
Author : Roger Temam
Publisher : American Mathematical Soc.
ISBN 13 : 0821827375
Total Pages : 426 pages
Book Rating : 4.8/5 (218 download)
Download or read book Navier-Stokes Equations written by Roger Temam and published by American Mathematical Soc.. This book was released on 2001-04-10 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1977, the book is devoted to the theory and numerical analysis of the Navier-Stokes equations for viscous incompressible fluid. On the theoretical side, results related to the existence, the uniqueness, and, in some cases, the regularity of solutions are presented. On the numerical side, various approaches to the approximation of Navier-Stokes problems by discretization are considered, such as the finite dereference method, the finite element method, and the fractional steps method. The problems of stability and convergence for numerical methods are treated as completely as possible. The new material in the present book (as compared to the preceding 1984 edition) is an appendix reproducing a survey article written in 1998. This appendix touches upon a few aspects not addressed in the earlier editions, in particular a short derivation of the Navier-Stokes equations from the basic conservation principles in continuum mechanics, further historical perspectives, and indications on new developments in the area. The appendix also surveys some aspects of the related Euler equations and the compressible Navier-Stokes equations. The book is written in the style of a textbook and the author has attempted to make the treatment self-contained. It can be used as a textbook or a reference book for researchers. Prerequisites for reading the book include some familiarity with the Navier-Stokes equations and some knowledge of functional analysis and Sololev spaces.
Author : Gregory Seregin
Publisher : World Scientific
ISBN 13 : 9814623423
Total Pages : 269 pages
Book Rating : 4.8/5 (146 download)
Download or read book Lecture Notes On Regularity Theory For The Navier-stokes Equations written by Gregory Seregin and published by World Scientific. This book was released on 2014-09-16 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lecture notes in this book are based on the TCC (Taught Course Centre for graduates) course given by the author in Trinity Terms of 2009-2011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the Navier-Stokes equations as well as the modern regularity theory for them. The latter is developed by means of the classical PDE's theory in the style that is quite typical for St Petersburg's mathematical school of the Navier-Stokes equations.The global unique solvability (well-posedness) of initial boundary value problems for the Navier-Stokes equations is in fact one of the seven Millennium problems stated by the Clay Mathematical Institute in 2000. It has not been solved yet. However, a deep connection between regularity and well-posedness is known and can be used to attack the above challenging problem. This type of approach is not very well presented in the modern books on the mathematical theory of the Navier-Stokes equations. Together with introduction chapters, the lecture notes will be a self-contained account on the topic from the very basic stuff to the state-of-art in the field.
Author : Pierre Gilles Lemarie-Rieusset
Publisher : CRC Press
ISBN 13 : 9781420035674
Total Pages : 412 pages
Book Rating : 4.0/5 (356 download)
Download or read book Recent developments in the Navier-Stokes problem written by Pierre Gilles Lemarie-Rieusset and published by CRC Press. This book was released on 2002-04-26 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Navier-Stokes equations: fascinating, fundamentally important, and challenging,. Although many questions remain open, progress has been made in recent years. The regularity criterion of Caffarelli, Kohn, and Nirenberg led to many new results on existence and non-existence of solutions, and the very active search for mild solutions in the 1990's culminated in the theorem of Koch and Tataru that, in some ways, provides a definitive answer. Recent Developments in the Navier-Stokes Problem brings these and other advances together in a self-contained exposition presented from the perspective of real harmonic analysis. The author first builds a careful foundation in real harmonic analysis, introducing all the material needed for his later discussions. He then studies the Navier-Stokes equations on the whole space, exploring previously scattered results such as the decay of solutions in space and in time, uniqueness, self-similar solutions, the decay of Lebesgue or Besov norms of solutions, and the existence of solutions for a uniformly locally square integrable initial value. Many of the proofs and statements are original and, to the extent possible, presented in the context of real harmonic analysis. Although the existence, regularity, and uniqueness of solutions to the Navier-Stokes equations continue to be a challenge, this book is a welcome opportunity for mathematicians and physicists alike to explore the problem's intricacies from a new and enlightening perspective.
Author :
Publisher : World Scientific
ISBN 13 :
Total Pages : 1001 pages
Book Rating : 4./5 ( download)
Download or read book written by and published by World Scientific. This book was released on with total page 1001 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gregory Seregin
Publisher : World Scientific Publishing Company Incorporated
ISBN 13 : 9789814623407
Total Pages : 258 pages
Book Rating : 4.6/5 (234 download)
Download or read book Lecture Notes on Regularity Theory for the Navier-Stokes Equations written by Gregory Seregin and published by World Scientific Publishing Company Incorporated. This book was released on 2014 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lecture notes in this book are based on the TCC (Taught Course Centre for graduates) course given by the author in Trinity Terms of 2009-2011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the Navier-Stokes equations as well as the modern regularity theory for them. The latter is developed by means of the classical PDE's theory in the style that is quite typical for St Petersburg's mathematical school of the Navier-Stokes equations. The global unique solvability (well-posedness) of initial boundary value problems for the Navier-Stokes equations is in fact one of the seven Millennium problems stated by the Clay Mathematical Institute in 2000. It has not been solved yet. However, a deep connection between regularity and well-posedness is known and can be used to attack the above challenging problem. This type of approach is not very well presented in the modern books on the mathematical theory of the Navier-Stokes equations. Together with introduction chapters, the lecture notes will be a self-contained account on the topic from the very basic stuff to the state-of-art in the field.
Author : Sergei Kuksin
Publisher : Cambridge University Press
ISBN 13 : 113957695X
Total Pages : 337 pages
Book Rating : 4.1/5 (395 download)
Download or read book Mathematics of Two-Dimensional Turbulence written by Sergei Kuksin and published by Cambridge University Press. This book was released on 2012-09-20 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to the mathematical study of two-dimensional statistical hydrodynamics and turbulence, described by the 2D Navier–Stokes system with a random force. The authors' main goal is to justify the statistical properties of a fluid's velocity field u(t,x) that physicists assume in their work. They rigorously prove that u(t,x) converges, as time grows, to a statistical equilibrium, independent of initial data. They use this to study ergodic properties of u(t,x) – proving, in particular, that observables f(u(t,.)) satisfy the strong law of large numbers and central limit theorem. They also discuss the inviscid limit when viscosity goes to zero, normalising the force so that the energy of solutions stays constant, while their Reynolds numbers grow to infinity. They show that then the statistical equilibria converge to invariant measures of the 2D Euler equation and study these measures. The methods apply to other nonlinear PDEs perturbed by random forces.
Author : John Groves Heywood
Publisher : World Scientific
ISBN 13 : 9789810233006
Total Pages : 256 pages
Book Rating : 4.2/5 (33 download)
Download or read book Theory of the Navier-Stokes Equations written by John Groves Heywood and published by World Scientific. This book was released on 1998 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects the articles presented at the Third International Conference on ?The Navier-Stokes Equations: Theory and Numerical Methods?, held in Oberwolfach, Germany. The articles are important contributions to a wide variety of topics in the Navier-Stokes theory: general boundary conditions, flow exterior to an obstacle, conical boundary points, the controllability of solutions, compressible flow, non-Newtonian flow, magneto-hydrodynamics, thermal convection, the interaction of fluids with elastic solids, the regularity of solutions, and Rothe's method of approximation.
Author : Jiri Neustupa
Publisher : Birkhäuser
ISBN 13 : 3034882432
Total Pages : 271 pages
Book Rating : 4.0/5 (348 download)
Download or read book Mathematical Fluid Mechanics written by Jiri Neustupa and published by Birkhäuser. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical modeling and numerical simulation in fluid mechanics are topics of great importance both in theory and technical applications. The present book attempts to describe the current status in various areas of research. The 10 chapters, mostly survey articles, are written by internationally renowned specialists and offer a range of approaches to and views of the essential questions and problems. In particular, the theories of incompressible and compressible Navier-Stokes equations are considered, as well as stability theory and numerical methods in fluid mechanics. Although the book is primarily written for researchers in the field, it will also serve as a valuable source of information to graduate students.
Author : Rodolfo Salvi
Publisher : CRC Press
ISBN 13 : 0824744896
Total Pages : 337 pages
Book Rating : 4.8/5 (247 download)
Download or read book The Navier-Stokes Equations written by Rodolfo Salvi and published by CRC Press. This book was released on 2001-09-27 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Contains proceedings of Varenna 2000, the international conference on theory and numerical methods of the navier-Stokes equations, held in Villa Monastero in Varenna, Lecco, Italy, surveying a wide range of topics in fluid mechanics, including compressible, incompressible, and non-newtonian fluids, the free boundary problem, and hydrodynamic potential theory."
Author : Tai-Peng Tsai
Publisher : American Mathematical Soc.
ISBN 13 : 1470430967
Total Pages : 239 pages
Book Rating : 4.4/5 (74 download)
Download or read book Lectures on Navier-Stokes Equations written by Tai-Peng Tsai and published by American Mathematical Soc.. This book was released on 2018-08-09 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a graduate text on the incompressible Navier-Stokes system, which is of fundamental importance in mathematical fluid mechanics as well as in engineering applications. The goal is to give a rapid exposition on the existence, uniqueness, and regularity of its solutions, with a focus on the regularity problem. To fit into a one-year course for students who have already mastered the basics of PDE theory, many auxiliary results have been described with references but without proofs, and several topics were omitted. Most chapters end with a selection of problems for the reader. After an introduction and a careful study of weak, strong, and mild solutions, the reader is introduced to partial regularity. The coverage of boundary value problems, self-similar solutions, the uniform L3 class including the celebrated Escauriaza-Seregin-Šverák Theorem, and axisymmetric flows in later chapters are unique features of this book that are less explored in other texts. The book can serve as a textbook for a course, as a self-study source for people who already know some PDE theory and wish to learn more about Navier-Stokes equations, or as a reference for some of the important recent developments in the area.
