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Mathematical Analysis of the Navier-Stokes Equations

2020-04-28 Mathematics
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Release : 2020-04-28
Genre : Mathematics
Kind : eBook
Book Rating : 264/5 ( reviews)

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Book Synopsis Mathematical Analysis of the Navier-Stokes Equations by : Matthias Hieber

Download or read book Mathematical Analysis of the Navier-Stokes Equations written by Matthias Hieber. This book was released on 2020-04-28. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations andRelated Models

2012-11-06 Mathematics
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Release : 2012-11-06
Genre : Mathematics
Kind : eBook
Book Rating : 753/5 ( reviews)

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Book Synopsis Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations andRelated Models by : Franck Boyer

Download or read book Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations andRelated Models written by Franck Boyer. This book was released on 2012-11-06. Available in PDF, EPUB and Kindle. Book excerpt: 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. .

Applied Analysis of the Navier-Stokes Equations

1995 Mathematics
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Release : 1995
Genre : Mathematics
Kind : eBook
Book Rating : 689/5 ( reviews)

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Book Synopsis Applied Analysis of the Navier-Stokes Equations by : Charles R. Doering

Download or read book Applied Analysis of the Navier-Stokes Equations written by Charles R. Doering. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on Navier-Stokes Equations

2018-08-09 Mathematics
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Release : 2018-08-09
Genre : Mathematics
Kind : eBook
Book Rating : 967/5 ( reviews)

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Book Synopsis Lectures on Navier-Stokes Equations by : Tai-Peng Tsai

Download or read book Lectures on Navier-Stokes Equations written by Tai-Peng Tsai. This book was released on 2018-08-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Navier–Stokes Equations

2016-04-12 Mathematics
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Release : 2016-04-12
Genre : Mathematics
Kind : eBook
Book Rating : 60X/5 ( reviews)

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Book Synopsis Navier–Stokes Equations by : Grzegorz Łukaszewicz

Download or read book Navier–Stokes Equations written by Grzegorz Łukaszewicz. This book was released on 2016-04-12. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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