The Three-Dimensional Navier–Stokes Equations

Classical Theory

Author: James C. Robinson,José L. Rodrigo,Witold Sadowski

Publisher: Cambridge University Press

ISBN: 1316715124

Category: Mathematics

Page: N.A

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A rigorous but accessible introduction to the mathematical theory of the three-dimensional Navier–Stokes equations, this book provides self-contained proofs of some of the most significant results in the area, many of which can only be found in research papers. Highlights include the existence of global-in-time Leray–Hopf weak solutions and the local existence of strong solutions; the conditional local regularity results of Serrin and others; and the partial regularity results of Caffarelli, Kohn, and Nirenberg. Appendices provide background material and proofs of some 'standard results' that are hard to find in the literature. A substantial number of exercises are included, with full solutions given at the end of the book. As the only introductory text on the topic to treat all of the mainstream results in detail, this book is an ideal text for a graduate course of one or two semesters. It is also a useful resource for anyone working in mathematical fluid dynamics.
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Lectures on Navier-Stokes Equations

Author: Tai-Peng Tsai

Publisher: American Mathematical Soc.

ISBN: 1470430967

Category: Fluid dynamics

Page: 224

View: 9290

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This book is a graduate text on the incompressible Navier-Stokes system, which is of fundamental importance in mathematical fluid mechanics as well as in engineering applications. The goal is to give a rapid exposition on the existence, uniqueness, and regularity of its solutions, with a focus on the regularity problem. To fit into a one-year course for students who have already mastered the basics of PDE theory, many auxiliary results have been described with references but without proofs, and several topics were omitted. Most chapters end with a selection of problems for the reader. After an introduction and a careful study of weak, strong, and mild solutions, the reader is introduced to partial regularity. The coverage of boundary value problems, self-similar solutions, the uniform L3 class including the celebrated Escauriaza-Seregin-Šverák Theorem, and axisymmetric flows in later chapters are unique features of this book that are less explored in other texts. The book can serve as a textbook for a course, as a self-study source for people who already know some PDE theory and wish to learn more about Navier-Stokes equations, or as a reference for some of the important recent developments in the area.
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Partial Differential Equations in Fluid Mechanics

Author: Charles L. Fefferman,James C. Robinson,José L. Rodrigo

Publisher: Cambridge University Press

ISBN: 1108573592

Category: Mathematics

Page: N.A

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The Euler and Navier–Stokes equations are the fundamental mathematical models of fluid mechanics, and their study remains central in the modern theory of partial differential equations. This volume of articles, derived from the workshop 'PDEs in Fluid Mechanics' held at the University of Warwick in 2016, serves to consolidate, survey and further advance research in this area. It contains reviews of recent progress and classical results, as well as cutting-edge research articles. Topics include Onsager's conjecture for energy conservation in the Euler equations, weak-strong uniqueness in fluid models and several chapters address the Navier–Stokes equations directly; in particular, a retelling of Leray's formative 1934 paper in modern mathematical language. The book also covers more general PDE methods with applications in fluid mechanics and beyond. This collection will serve as a helpful overview of current research for graduate students new to the area and for more established researchers.
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Vorticity and Incompressible Flow

Author: Andrew J. Majda,Andrea L. Bertozzi

Publisher: Cambridge University Press

ISBN: 9780521639484

Category: Mathematics

Page: 545

View: 9499

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This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. While the contents center on mathematical theory, many parts of the book showcase the interaction between rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprise a modern applied mathematics graduate course on the weak solution theory for incompressible flow.
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Vortex Methods

Theory and Practice

Author: Georges-Henri Cottet,Petros D. Koumoutsakos

Publisher: Cambridge University Press

ISBN: 0521621860

Category: Mathematics

Page: 313

View: 8059

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Vortex methods have matured in recent years, offering an interesting alternative to finite difference and spectral methods for high resolution numerical solutions of the Navier Stokes equations. In the past three decades, research into the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character, which was the motivation for their introduction. This book presents and analyzes vortex methods as a tool for the direct numerical simulation of impressible viscous flows. It will interest graduate students and researchers in numerical analysis and fluid mechanics and also serve as an ideal textbook for courses in fluid dynamics.
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Nonlinear Evolutionary Partial Differential Equations

International Conference on Nonlinear Evolutionary Partial Differential Equations, June 21-25, 1993, Beijing, People's Republic of China

Author: Xiaxi Ding,Tai-Ping Liu

Publisher: American Mathematical Soc.

ISBN: 0821806610

Category: Mathematics

Page: 637

View: 3689

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This volume contains the proceedings from the International Conference on Nonlinear Evolutionary Partial Differential Equations held in Beijing in June 1993. The topic for the conference was selected because of its importance in the natural sciences and for its mathematical significance. Discussion topics include conservation laws, dispersion waves, Einstein's theory of gravitation, reaction-diffusion equations, the Navier-Stokes equations, and more. New results were presented and are featured in this volume. Titles in this series are co-published with International Press, Cambridge, MA.
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