The Navier Stokes Problem In The 21st Century

Author : Pierre Gilles Lemarie-Rieusset
Publisher : CRC Press
Page : 718 pages
File Size : 53,5 Mb
Release : 2018-09-03
Category : Mathematics
ISBN : 9781315362731

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The Navier-Stokes Problem in the 21st Century by Pierre Gilles Lemarie-Rieusset Pdf

Up-to-Date Coverage of the Navier–Stokes Equation from an Expert in Harmonic Analysis The complete resolution of the Navier–Stokes equation—one of the Clay Millennium Prize Problems—remains an important open challenge in partial differential equations (PDEs) research despite substantial studies on turbulence and three-dimensional fluids. The Navier–Stokes Problem in the 21st Century provides a self-contained guide to the role of harmonic analysis in the PDEs of fluid mechanics. The book focuses on incompressible deterministic Navier–Stokes equations in the case of a fluid filling the whole space. It explores the meaning of the equations, open problems, and recent progress. It includes classical results on local existence and studies criterion for regularity or uniqueness of solutions. The book also incorporates historical references to the (pre)history of the equations as well as recent references that highlight active mathematical research in the field.

Author : Pierre Gilles Lemarié
Publisher : C&h/CRC Press
Page : 0 pages
File Size : 51,9 Mb
Release : 2024
Category : Fluid dynamics
ISBN : 103262373X

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The Navier-Stokes Problem in the 21st Century by Pierre Gilles Lemarié Pdf

"The complete resolution of the Navier-Stokes equation-one of the Clay Millennium Prize Problems-remains an important open challenge in partial differential equations (PDEs) research despite substantial studies on turbulence and three-dimensional fluids. The Navier-Stokes Problem in the 21st Century, Second Edition continues to provide a self-contained guide to the role of harmonic analysis in the PDEs of fluid mechanics, now revised to include fresh examples, theorems, results, and references that have become relevant since the first edition published in 2016"--

Author : Roger Temam
Publisher : American Mathematical Soc.
Page : 426 pages
File Size : 42,9 Mb
Release : 2001-04-10
Category : Mathematics
ISBN : 9780821827376

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Navier-Stokes Equations by Roger Temam Pdf

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 : Hermann Sohr
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 48,6 Mb
Release : 2012-12-13
Category : Mathematics
ISBN : 9783034805513

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The Navier-Stokes Equations by Hermann Sohr Pdf

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 : P. G. Drazin,N. Riley
Publisher : Cambridge University Press
Page : 212 pages
File Size : 54,5 Mb
Release : 2006-05-25
Category : Mathematics
ISBN : 0521681626

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The Navier-Stokes Equations by P. G. Drazin,N. Riley Pdf

This 2006 book details exact solutions to the Navier-Stokes equations for senior undergraduates and graduates or research reference.

Author : Alexander G. Ramm
Publisher : Springer Nature
Page : 61 pages
File Size : 47,6 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 9783031024313

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The Navier–Stokes Problem by Alexander G. Ramm Pdf

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.

Author : David Canright,Geoffrey B Mcfadden,Michael J Miksis,G P Neitzel,Marc K Smith
Publisher : World Scientific
Page : 332 pages
File Size : 46,6 Mb
Release : 2002-05-30
Category : Technology & Engineering
ISBN : 9781783261246

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Interfaces For The 21st Century: New Research Directions In Fluid Mechanics And Materials Science by David Canright,Geoffrey B Mcfadden,Michael J Miksis,G P Neitzel,Marc K Smith Pdf

This book highlights some recent advances in interfacial research in the fields of fluid mechanics and materials science at the beginning of the twenty-first century. It is an extension of the presentations made during the conference “Interfaces for the 21st Century,” held on August 16-18, 1999, in Monterey, California. It includes papers by sixteen renowned experts in the field of interfacial mechanics, abstracts contributed by research scientists, and a summary of a panel discussion on future research directions. The book covers experimental and theoretical approaches, with the unifying philosophy being the investigation of new techniques for modeling the dynamics of interfaces. A number of new and exciting solution methods and experimental studies, as well as the physical problems that initiated them, are presented.

Author : Pierre Gilles Lemarie-Rieusset
Publisher : CRC Press
Page : 412 pages
File Size : 54,8 Mb
Release : 2002-04-26
Category : Mathematics
ISBN : 1420035673

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Recent developments in the Navier-Stokes problem by Pierre Gilles Lemarie-Rieusset Pdf

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 : M-O. Bristeau
Publisher : Wiley-Blackwell
Page : 906 pages
File Size : 49,8 Mb
Release : 1997-04-30
Category : Computers
ISBN : STANFORD:36105022399187

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Computational Science for the 21st Century by M-O. Bristeau Pdf

Computational science can loosely be defined as the endeavor to develop and analyse models for the simulation and control of complex processes. This is achieved by making optimal use of computer resources and by drawing upon a variety of disciplines, techniques and theories. With the emergence of advanced computational and information technologies, computational science now has a significant impact on engineering, physical, biological, management and social sciences. The contributions in this state-of-the-art volume range from theoretical and numerical topics to practical implementations. The subject matter includes modelling, mathematical and numerical analysis, differential equations, linear algebra, optimization, domain decomposition, computational fluid dynamics, computational mechanics, elasticity, structure, computational physics and chemistry, electromagnetic, control theory and other applications. This volume is dedicated to Roland Glowinski on the occasion of his 60th birthday. It is aimed at the next generation of scientists, applied mathematicians, computer scientists, practitioners and engineers who will define computational science within the context of the challenging scientific, industrial, economic and societal problems of the 21st century.

Author : Stephen Childress
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 53,6 Mb
Release : 2009-10-09
Category : Science
ISBN : 9780821848883

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An Introduction to Theoretical Fluid Mechanics by Stephen Childress Pdf

This book gives an overview of classical topics in fluid dynamics, focusing on the kinematics and dynamics of incompressible inviscid and Newtonian viscous fluids, but also including some material on compressible flow. The topics are chosen to illustrate the mathematical methods of classical fluid dynamics. The book is intended to prepare the reader for more advanced topics of current research interest.

Author : Terence Tao
Publisher : Hindustan Book Agency
Page : 0 pages
File Size : 47,8 Mb
Release : 2016-09-26
Category : Mathematics
ISBN : 9380250657

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Analysis II by Terence Tao Pdf

This is part two of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.

Author : Anonim
Publisher : Unknown
Page : 458 pages
File Size : 40,9 Mb
Release : 2003
Category : Energy development
ISBN : UOM:39015061551621

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4th International R&D Conference, Water and Energy for 21st Century, 28-31 January 2003, Aurangabad, Maharashtra: Water resources by Anonim Pdf

Chiefly with reference to India.

Author : Anonim
Publisher : Unknown
Page : 434 pages
File Size : 51,9 Mb
Release : 1995
Category : Helicopters
ISBN : PSU:000043536740

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Aeromechanics Technology & Product Design for the 21st Century by Anonim Pdf

Author : S. Friedlander,D. Serre
Publisher : Gulf Professional Publishing
Page : 627 pages
File Size : 50,7 Mb
Release : 2003-03-27
Category : Science
ISBN : 9780080533544

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Handbook of Mathematical Fluid Dynamics by S. Friedlander,D. Serre Pdf

The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.

Author : Solomon I. Khmelnik
Publisher : Lulu.com
Page : 134 pages
File Size : 44,6 Mb
Release : 2011
Category : Electronic
ISBN : 9781458324009

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Navier-Stokes equations. On the existence and the search method for global solutions. by Solomon I. Khmelnik Pdf