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Author : Charles R. Doering
Publisher : Cambridge University Press
Page : 236 pages
File Size : 17,53 MB
Release : 1995
Category : Mathematics
ISBN : 9780521445689
This introductory physical and mathematical presentation of the Navier-Stokes equations focuses on unresolved questions of the regularity of solutions in three spatial dimensions, and the relation of these issues to the physical phenomenon of turbulent fluid motion.
Author : Denise Campos (Editor)
Publisher :
Page : 508 pages
File Size : 10,13 MB
Release : 2016
Category : MATHEMATICS
ISBN : 9781536103083
Author : Denise Campos
Publisher : Nova Science Publishers
Page : 0 pages
File Size : 30,67 MB
Release : 2016-12
Category : Fluid dynamics
ISBN : 9781536102925
NavierStokes equations describe the motion of fluids; they arise from applying Newtons second law of motion to a continuous function that represents fluid flow. If we apply the assumption that stress in the fluid is the sum of a pressure term and a diffusing viscous term, which is proportional to the gradient of velocity, we arrive at a set of equations that describe viscous flow. This handbook provides new research on the theories and applied analysis of Navier-Stokes Equations.
Author : Matthias Hieber
Publisher : Springer Nature
Page : 471 pages
File Size : 30,69 MB
Release : 2020-04-28
Category : Mathematics
ISBN : 3030362264
This book collects together a unique set of articles dedicated to several fundamental aspects of the Navier–Stokes equations. As is well known, understanding the mathematical properties of these equations, along with their physical interpretation, constitutes one of the most challenging questions of applied mathematics. Indeed, the Navier-Stokes equations feature among the Clay Mathematics Institute's seven Millennium Prize Problems (existence of global in time, regular solutions corresponding to initial data of unrestricted magnitude). The text comprises three extensive contributions covering the following topics: (1) Operator-Valued H∞-calculus, R-boundedness, Fourier multipliers and maximal Lp-regularity theory for a large, abstract class of quasi-linear evolution problems with applications to Navier–Stokes equations and other fluid model equations; (2) Classical existence, uniqueness and regularity theorems of solutions to the Navier–Stokes initial-value problem, along with space-time partial regularity and investigation of the smoothness of the Lagrangean flow map; and (3) A complete mathematical theory of R-boundedness and maximal regularity with applications to free boundary problems for the Navier–Stokes equations with and without surface tension. Offering a general mathematical framework that could be used to study fluid problems and, more generally, a wide class of abstract evolution equations, this volume is aimed at graduate students and researchers who want to become acquainted with fundamental problems related to the Navier–Stokes equations.
Author : Franck Boyer
Publisher : Springer Science & Business Media
Page : 538 pages
File Size : 47,27 MB
Release : 2012-11-06
Category : Mathematics
ISBN : 1461459753
The objective of this self-contained book is two-fold. First, the reader is introduced to the modelling and mathematical analysis used in fluid mechanics, especially concerning the Navier-Stokes equations which is the basic model for the flow of incompressible viscous fluids. Authors introduce mathematical tools so that the reader is able to use them for studying many other kinds of partial differential equations, in particular nonlinear evolution problems. The background needed are basic results in calculus, integration, and functional analysis. Some sections certainly contain more advanced topics than others. Nevertheless, the authors’ aim is that graduate or PhD students, as well as researchers who are not specialized in nonlinear analysis or in mathematical fluid mechanics, can find a detailed introduction to this subject. .
Author : Roger Temam
Publisher : SIAM
Page : 147 pages
File Size : 25,24 MB
Release : 1995-01-01
Category : Technology & Engineering
ISBN : 0898713404
This second edition attempts to arrive as simply as possible at some central problems in the Navier-Stokes equations.
Author : Peter Constantin
Publisher : University of Chicago Press
Page : 200 pages
File Size : 40,8 MB
Release : 1988
Category : Mathematics
ISBN : 0226115496
Lecture notes of graduate courses given by the authors at Indiana University (1985-86) and the University of Chicago (1986-87). Paper edition, $14.95. Annotation copyright Book News, Inc. Portland, Or.
Author : Grzegorz Łukaszewicz
Publisher : Springer
Page : 395 pages
File Size : 14,55 MB
Release : 2016-04-12
Category : Mathematics
ISBN : 331927760X
This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from advanced undergraduate students to engineers and professional mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier–Stokes equations. Incompressible Navier–Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior of the fluid, assuming knowledge of its initial and boundary states. These equations are one of the most important models of mathematical physics: although they have been a subject of vivid research for more than 150 years, there are still many open problems due to the nature of nonlinearity present in the equations. The nonlinear convective term present in the equations leads to phenomena such as eddy flows and turbulence. In particular, the question of solution regularity for three-dimensional problem was appointed by Clay Institute as one of the Millennium Problems, the key problems in modern mathematics. The problem remains challenging and fascinating for mathematicians, and the applications of the Navier–Stokes equations range from aerodynamics (drag and lift forces), to the design of watercraft and hydroelectric power plants, to medical applications such as modeling the flow of blood in the circulatory system.
Author : Roger Temam
Publisher : SIAM
Page : 155 pages
File Size : 17,59 MB
Release : 1995-01-01
Category : Technology & Engineering
ISBN : 9781611970050
This second edition, like the first, attempts to arrive as simply as possible at some central problems in the Navier-Stokes equations in the following areas: existence, uniqueness, and regularity of solutions in space dimensions two and three; large time behavior of solutions and attractors; and numerical analysis of the Navier-Stokes equations. Since publication of the first edition of these lectures in 1983, there has been extensive research in the area of inertial manifolds for Navier-Stokes equations. These developments are addressed in a new section devoted entirely to inertial manifolds. Inertial manifolds were first introduced under this name in 1985 and, since then, have been systematically studied for partial differential equations of the Navier-Stokes type. Inertial manifolds are a global version of central manifolds. When they exist they encompass the complete dynamics of a system, reducing the dynamics of an infinite system to that of a smooth, finite-dimensional one called the inertial system. Although the theory of inertial manifolds for Navier-Stokes equations is not complete at this time, there is already a very interesting and significant set of results which deserves to be known, in the hope that it will stimulate further research in this area. These results are reported in this edition.
Author : Pierre Gilles Lemarie-Rieusset
Publisher : CRC Press
Page : 412 pages
File Size : 33,40 MB
Release : 2002-04-26
Category : Mathematics
ISBN : 9781420035674
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.