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Author : Wolf von Wahl
Publisher : Springer-Verlag
ISBN 13 : 3663139115
Total Pages : 289 pages
Book Rating : 4.6/5 (631 download)
Download or read book The Equations of Navier-Stokes and Abstract Parabolic Equations written by Wolf von Wahl and published by Springer-Verlag. This book was released on 2013-07-02 with total page 289 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 : Heinz-Otto Kreiss
Publisher : SIAM
ISBN 13 : 0898719135
Total Pages : 408 pages
Book Rating : 4.8/5 (987 download)
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.
Author : Atsushi Yagi
Publisher : Springer Science & Business Media
ISBN 13 : 3642046312
Total Pages : 594 pages
Book Rating : 4.6/5 (42 download)
Download or read book Abstract Parabolic Evolution Equations and their Applications written by Atsushi Yagi and published by Springer Science & Business Media. This book was released on 2009-11-03 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is intended to present the fundamentals of the theory of abstract parabolic evolution equations and to show how to apply to various nonlinear dif- sion equations and systems arising in science. The theory gives us a uni?ed and s- tematic treatment for concrete nonlinear diffusion models. Three main approaches are known to the abstract parabolic evolution equations, namely, the semigroup methods, the variational methods, and the methods of using operational equations. In order to keep the volume of the monograph in reasonable length, we will focus on the semigroup methods. For other two approaches, see the related references in Bibliography. The semigroup methods, which go back to the invention of the analytic se- groups in the middle of the last century, are characterized by precise formulas representing the solutions of the Cauchy problem for evolution equations. The ?tA analytic semigroup e generated by a linear operator ?A provides directly a fundamental solution to the Cauchy problem for an autonomous linear e- dU lution equation, +AU =F(t), 0
Author : Jan Prüss
Publisher : Birkhäuser
ISBN 13 : 3319276980
Total Pages : 618 pages
Book Rating : 4.3/5 (192 download)
Download or read book Moving Interfaces and Quasilinear Parabolic Evolution Equations written by Jan Prüss and published by Birkhäuser. This book was released on 2016-07-25 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.
Author : Jan W. Cholewa
Publisher : Cambridge University Press
ISBN 13 : 0521794242
Total Pages : 252 pages
Book Rating : 4.5/5 (217 download)
Download or read book Global Attractors in Abstract Parabolic Problems written by Jan W. Cholewa and published by Cambridge University Press. This book was released on 2000-08-31 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the asymptotic behaviour of dynamical systems corresponding to parabolic equations.
Author : Viorel Barbu
Publisher : Springer Science & Business Media
ISBN 13 : 0857290436
Total Pages : 285 pages
Book Rating : 4.8/5 (572 download)
Download or read book Stabilization of Navier–Stokes Flows written by Viorel Barbu and published by Springer Science & Business Media. This book was released on 2010-11-19 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stabilization of Navier–Stokes Flows presents recent notable progress in the mathematical theory of stabilization of Newtonian fluid flows. Finite-dimensional feedback controllers are used to stabilize exponentially the equilibrium solutions of Navier–Stokes equations, reducing or eliminating turbulence. Stochastic stabilization and robustness of stabilizable feedback are also discussed. The analysis developed here provides a rigorous pattern for the design of efficient stabilizable feedback controllers to meet the needs of practical problems and the conceptual controllers actually detailed will render the reader’s task of application easier still. Stabilization of Navier–Stokes Flows avoids the tedious and technical details often present in mathematical treatments of control and Navier–Stokes equations and will appeal to a sizeable audience of researchers and graduate students interested in the mathematics of flow and turbulence control and in Navier-Stokes equations in particular.
Author : Tomasz W. Dłotko
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311059868X
Total Pages : 217 pages
Book Rating : 4.1/5 (15 download)
Download or read book Critical Parabolic-Type Problems written by Tomasz W. Dłotko and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-05 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book covers the theory of semilinear equations with sectorial operator going back to the studies of Yosida, Henry, and Pazy, which are deeply extended nowadays. The treatment emphasizes existence-uniqueness theory as a topic of functional analysis and examines abstract evolutionary equations, with applications to the Navier-Stokes system, the quasi-geostrophic equation, and fractional reaction-diffusion equations.
Author : Alessandra Lunardi
Publisher : Springer Science & Business Media
ISBN 13 : 3034805578
Total Pages : 437 pages
Book Rating : 4.0/5 (348 download)
Download or read book Analytic Semigroups and Optimal Regularity in Parabolic Problems written by Alessandra Lunardi and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems. Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones. Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived. The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in parabolic partial differential equations and systems. It gives a comprehensive overview on the present state of the art in the field, teaching at the same time how to exploit its basic techniques. - - - This very interesting book provides a systematic treatment of the basic theory of analytic semigroups and abstract parabolic equations in general Banach spaces, and how this theory may be used in the study of parabolic partial differential equations; it takes into account the developments of the theory during the last fifteen years. (...) For instance, optimal regularity results are a typical feature of abstract parabolic equations; they are comprehensively studied in this book, and yield new and old regularity results for parabolic partial differential equations and systems. (Mathematical Reviews) Motivated by applications to fully nonlinear problems the approach is focused on classical solutions with continuous or Hölder continuous derivatives. (Zentralblatt MATH)
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 : R. Younsi
Publisher :
ISBN 13 : 9781613245903
Total Pages : 0 pages
Book Rating : 4.2/5 (459 download)
Download or read book Navier-Stokes Equations written by R. Younsi and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that the Navier -- Stokes equations are one of the pillars of fluid mechanics. These equations are useful because they describe the physics of many things of academic and economic interest. They may be used to model the weather behaviour, ocean currents, water flow in a pipe and air flow around a wing. The Navier -- Stokes equations in their full and simplified forms also help with the design of train, aircraft and cars, the study of blood flow, the design of power stations and pollution analysis. This book presents contributions on the application of Navier-Stokes in some engineering applications and provides a description of how the Navier-Stokes equations can be scaled.
Author : M.A. Shubin
Publisher : Springer Science & Business Media
ISBN 13 : 3642565794
Total Pages : 296 pages
Book Rating : 4.6/5 (425 download)
Download or read book Pseudodifferential Operators and Spectral Theory written by M.A. Shubin and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: I had mixed feelings when I thought how I should prepare the book for the second edition. It was clear to me that I had to correct all mistakes and misprints that were found in the book during the life of the first edition. This was easy to do because the mistakes were mostly minor and easy to correct, and the misprints were not many. It was more difficult to decide whether I should update the book (or at least its bibliography) somehow. I decided that it did not need much of an updating. The main value of any good mathematical book is that it teaches its reader some language and some skills. It can not exhaust any substantial topic no matter how hard the author tried. Pseudodifferential operators became a language and a tool of analysis of partial differential equations long ago. Therefore it is meaningless to try to exhaust this topic. Here is an easy proof. As of July 3, 2000, MathSciNet (the database of the American Mathematical Society) in a few seconds found 3695 sources, among them 363 books, during its search for "pseudodifferential operator". (The search also led to finding 963 sources for "pseudo-differential operator" but I was unable to check how much the results ofthese two searches intersected). This means that the corresponding words appear either in the title or in the review published in Mathematical Reviews.
Author : Hermann Sohr
Publisher : Birkhäuser
ISBN 13 : 3034882556
Total Pages : 375 pages
Book Rating : 4.0/5 (348 download)
Download or read book The Navier-Stokes Equations written by Hermann Sohr and published by Birkhäuser. This book was released on 2013-11-27 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an elementary, self-contained approach to the mathematical theory of viscous, incompressible fluid in a domain of the Euclidian space, described by the equations of Navier-Stokes. It is the first to provide a systematic treatment of the subject. It is designed for students familiar with basic tools in Hilbert and Banach spaces, but fundamental properties of, for example, Sobolev spaces, are collected in the first two chapters.
Author : Beatrice Riviere
Publisher : SIAM
ISBN 13 : 089871656X
Total Pages : 201 pages
Book Rating : 4.8/5 (987 download)
Download or read book Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations written by Beatrice Riviere and published by SIAM. This book was released on 2008-12-18 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on three primal DG methods, covering both theory and computation, and providing the basic tools for analysis.
Author : Herbert Amann
Publisher : Springer Science & Business Media
ISBN 13 : 9783764351144
Total Pages : 688 pages
Book Rating : 4.3/5 (511 download)
Download or read book Linear and Quasilinear Parabolic Problems written by Herbert Amann and published by Springer Science & Business Media. This book was released on 1995-03-27 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: This treatise gives an exposition of the functional analytical approach to quasilinear parabolic evolution equations, developed to a large extent by the author during the last 10 years. This approach is based on the theory of linear nonautonomous parabolic evolution equations and on interpolation-extrapolation techniques. It is the only general method that applies to noncoercive quasilinear parabolic systems under nonlinear boundary conditions. The present first volume is devoted to a detailed study of nonautonomous linear parabolic evolution equations in general Banach spaces. It contains a careful exposition of the constant domain case, leading to some improvements of the classical Sobolevskii-Tanabe results. It also includes recent results for equations possessing constant interpolation spaces. In addition, systematic presentations of the theory of maximal regularity in spaces of continuous and Hölder continuous functions, and in Lebesgue spaces, are given. It includes related recent theorems in the field of harmonic analysis in Banach spaces and on operators possessing bounded imaginary powers. Lastly, there is a complete presentation of the technique of interpolation-extrapolation spaces and of evolution equations in those spaces, containing many new results.
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 : John G. Heywood
Publisher : Springer
ISBN 13 : 3540471413
Total Pages : 245 pages
Book Rating : 4.5/5 (44 download)
Download or read book The Navier-Stokes Equations Theory and Numerical Methods written by John G. Heywood and published by Springer. This book was released on 2006-11-14 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings contain original (refereed) research articles by specialists from many countries, on a wide variety of aspects of Navier-Stokes equations. Additionally, 2 survey articles intended for a general readership are included: one surveys the present state of the subject via open problems, and the other deals with the interplay between theory and numerical analysis.
