Download or read book The Navier Stokes Problem in the 21st Century written by Pierre Gilles Lemarie-Rieusset and published by CRC Press. This book was released on 2018-09-03 with total page 718 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 The book also incorporates historical references to the (pre)history of the equations as well as recent references that highlight active mathematical research in the field.
Download or read book The Navier Stokes Problem in the 21st Century written by Pierre Gilles Lemarié and published by C&h/CRC Press. This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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"--
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.
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 367 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.
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.
Download or read book The Navier Stokes Equations written by P. G. Drazin and published by Cambridge University Press. This book was released on 2006-05-25 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2006 book details exact solutions to the Navier-Stokes equations for senior undergraduates and graduates or research reference.
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.
Download or read book Analysis written by Terence Tao and published by . This book was released on 2006 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an introduction to real analysis, this text is suitable for honours undergraduates. It starts at the very beginning - the construction of the number systems and set theory, then to the basics of analysis, through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral.
Download or read book Galileo Unbound written by David D. Nolte and published by Oxford University Press. This book was released on 2018-07-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.
Download or read book An Introduction to Theoretical Fluid Mechanics written by Stephen Childress and published by American Mathematical Soc.. This book was released on 2009-10-09 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Turbulence and Shell Models written by Peter D. Ditlevsen and published by Cambridge University Press. This book was released on 2010-10-28 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Turbulence is a huge subject of ongoing research. This book bridges the modern development in dynamical systems theory and the theory of fully developed turbulence. Many solved and unsolved problems in turbulence have equivalencies in simple dynamical models, which are much easier to handle analytically and numerically. This book gives a modern view of the subject by first giving the essentials of the theory of turbulence before moving on to shell models. These show much of the same complex behaviour as fluid turbulence, but are much easier to handle analytically and numerically. Any necessary maths is explained and self-contained, making this book ideal for advanced undergraduates and graduate students, as well as researchers and professionals, wanting to understand the basics of fully developed turbulence.
Download or read book The Turbulence Problem written by Michael Eckert and published by Springer Nature. This book was released on 2019-10-05 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the road toward a history of turbulence, this book focuses on what the actors in this research field have identified as the “turbulence problem”. Turbulent flow rose to prominence as one of the most persistent challenges in science. At different times and in different social and disciplinary settings, the nature of this problem has changed in response to changing research agendas. This book does not seek to provide a comprehensive account, but instead an exemplary exposition on the environments in which problems become the subjects of research agendas, with particular emphasis on the first half of the 20th century.
Download or read book Introduction to PDEs and Waves for the Atmosphere and Ocean written by Andrew Majda and published by American Mathematical Soc.. This book was released on 2003 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a leading specialist in the area of atmosphere/ocean science (AOS), the book presents an excellent introduction to this important topic. The goals of these lecture notes, based on courses presented by the author at the Courant Institute of Mathematical Sciences, are to introduce mathematicians to the fascinating and important area of atmosphere/ocean science (AOS) and, conversely, to develop a mathematical viewpoint on basic topics in AOS of interest to the disciplinary AOS community, ranging from graduate students to researchers. The lecture notes emphasize the serendipitous connections between applied mathematics and geophysical flows in the style of modern applied mathematics, where rigorous mathematical analysis as well as asymptotic, qualitative, and numerical modeling all interact to ease the understanding of physical phenomena. Reading these lecture notes does not require a previous course in fluid dynamics, although a serious reader should supplement these notes with material such The book is intended for graduate students and researchers working in interdisciplinary areas between mathematics and AOS. It is excellent for supplementary course reading or independent study.
Download or read book Handbook of Mathematical Fluid Dynamics written by S. Friedlander and published by Gulf Professional Publishing. This book was released on 2003-03-27 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Robust Numerical Methods for Singularly Perturbed Differential Equations written by Hans-Görg Roos and published by Springer Science & Business Media. This book was released on 2008-09-17 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.
Download or read book Interfaces For The 21st Century New Research Directions In Fluid Mechanics And Materials Science written by David Canright and published by World Scientific. This book was released on 2002-05-30 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
