On the Global Regularity Problem for the 3-dimensional Navier-Stokes Equations on Thin Domains
Author: Vadim Gene Bondarevsky
Publisher:
Published: 1996
Total Pages: 114
ISBN-13:
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Handbook of Mathematical Fluid Dynamics
Author: S. Friedlander
Publisher: Gulf Professional Publishing
Published: 2003-03-27
Total Pages: 627
ISBN-13: 008053354X
DOWNLOAD EBOOKThe 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.
Acta Numerica 2009
Author: Arieh Iserles
Publisher: Cambridge University Press
Published: 2009-05-28
Total Pages: 360
ISBN-13: 9780521192118
DOWNLOAD EBOOKA high-impact, prestigious, annual publication featuring invited surveys by subject leaders: essential reading for all practitioners and researchers.
Navier–Stokes Equations
Author: Roger Temam
Publisher: American Mathematical Society
Published: 2024-05-24
Total Pages: 426
ISBN-13: 1470477866
DOWNLOAD EBOOKOriginally 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.
Handbook of Dynamical Systems
Author: A. Katok
Publisher: Elsevier
Published: 2005-12-17
Total Pages: 1235
ISBN-13: 0080478220
DOWNLOAD EBOOKThis second half of Volume 1 of this Handbook follows Volume 1A, which was published in 2002. The contents of these two tightly integrated parts taken together come close to a realization of the program formulated in the introductory survey "Principal Structures of Volume 1A.The present volume contains surveys on subjects in four areas of dynamical systems: Hyperbolic dynamics, parabolic dynamics, ergodic theory and infinite-dimensional dynamical systems (partial differential equations).. Written by experts in the field.. The coverage of ergodic theory in these two parts of Volume 1 is considerably more broad and thorough than that provided in other existing sources. . The final cluster of chapters discusses partial differential equations from the point of view of dynamical systems.
Dynamics of Evolutionary Equations
Author: George R. Sell
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 680
ISBN-13: 1475750374
DOWNLOAD EBOOKThe theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. This book serves as an entrée for scholars beginning their journey into the world of dynamical systems, especially infinite dimensional spaces. The main approach involves the theory of evolutionary equations.
Global Special Regular Solutions to the Navier-Stokes Equations in Axially Symmetric Domains Under Boundary Slip Conditions
Author: Wojciech M. Zajączkowski
Publisher:
Published: 2005
Total Pages: 146
ISBN-13:
DOWNLOAD EBOOKLocal Feedback Regularization of Three-dimensional Navier-Stokes Equations on Bounded Domains
Author: Andras Balogh
Publisher:
Published: 1997
Total Pages: 116
ISBN-13:
DOWNLOAD EBOOKNavier–Stokes Equations
Author: Grzegorz Łukaszewicz
Publisher: Springer
Published: 2016-04-12
Total Pages: 395
ISBN-13: 331927760X
DOWNLOAD EBOOKThis 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.
Optimization Methods in Partial Differential Equations
Author: Steven Cox
Publisher: American Mathematical Soc.
Published: 1997
Total Pages: 362
ISBN-13: 0821806041
DOWNLOAD EBOOKThe problems considered range from basic theoretical issues in the calculus of variations - such as infinite dimensional Hamilton Jacobi equations, saddle point principles, and issues of unique continuation - to ones focusing on application and computation, where theoretical tools are tuned to more specifically defined problems.
