Lecture Notes On Regularity Theory For The Navier Stokes Equations
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Lecture Notes On Regularity Theory For The Navier Stokes Equations
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Author : Gregory Seregin
language : en
Publisher: World Scientific
Release Date : 2014-09-16
Lecture Notes On Regularity Theory For The Navier Stokes Equations written by Gregory Seregin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-16 with Mathematics categories.
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.
Regularity Theory For Generalized Navier Stokes Equations
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Author : Cholmin Sin
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-03-17
Regularity Theory For Generalized Navier Stokes Equations written by Cholmin Sin and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-17 with Mathematics categories.
This book delves into the recent findings and research methods in the existence and regularity theory for Non-Newtonian Fluids with Variable Power-Law. The aim of this book is not only to introduce recent results and research methods in the existence and regularity theory, such as higher integrability, higher differentiability, and Holder continuity for flows of non-Newtonian fluids with variable power-laws, but also to summarize much of the existing literature concerning these topics. While this book mainly focuses on steady-state flows of non-Newtonian fluids, the methods and ideas presented in this book can be applied to unsteady flows (as discussed in Chapter 7) and other related problems such as complex non-Newtonian fluids, plasticity, elasticity, p(x)-Laplacian type systems, and so on. The book is intended for researchers and graduate students in the field of mathematical fluid mechanics and partial differential equations with variable exponents. It is expected to contribute to the advancement of mathematics and its applications.
Lectures On Navier Stokes Equations
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Author : Tai-Peng Tsai
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-09
Lectures On Navier Stokes Equations written by Tai-Peng Tsai and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-09 with Mathematics categories.
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.
An Introduction To The Mathematical Theory Of The Navier Stokes Equations
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Author : Giovanni Galdi
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-12
An Introduction To The Mathematical Theory Of The Navier Stokes Equations written by Giovanni Galdi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-12 with Mathematics categories.
The book provides a comprehensive, detailed and self-contained treatment of the fundamental mathematical properties of boundary-value problems related to the Navier-Stokes equations. These properties include existence, uniqueness and regularity of solutions in bounded as well as unbounded domains. Whenever the domain is unbounded, the asymptotic behavior of solutions is also investigated. This book is the new edition of the original two volume book, under the same title, published in 1994. In this new edition, the two volumes have merged into one and two more chapters on steady generalized oseen flow in exterior domains and steady Navier–Stokes flow in three-dimensional exterior domains have been added. Most of the proofs given in the previous edition were also updated. An introductory first chapter describes all relevant questions treated in the book and lists and motivates a number of significant and still open questions. It is written in an expository style so as to be accessible also to non-specialists.Each chapter is preceded by a substantial, preliminary discussion of the problems treated, along with their motivation and the strategy used to solve them. Also, each chapter ends with a section dedicated to alternative approaches and procedures, as well as historical notes. The book contains more than 400 stimulating exercises, at different levels of difficulty, that will help the junior researcher and the graduate student to gradually become accustomed with the subject. Finally, the book is endowed with a vast bibliography that includes more than 500 items. Each item brings a reference to the section of the book where it is cited. The book will be useful to researchers and graduate students in mathematics in particular mathematical fluid mechanics and differential equations. Review of First Edition, First Volume: “The emphasis of this book is on an introduction to the mathematical theory of the stationary Navier-Stokes equations. It is written in the style of a textbook and is essentially self-contained. The problems are presented clearly and in an accessible manner. Every chapter begins with a good introductory discussion of the problems considered, and ends with interesting notes on different approaches developed in the literature. Further, stimulating exercises are proposed. (Mathematical Reviews, 1995)
The Partial Regularity Theory Of Caffarelli Kohn And Nirenberg And Its Sharpness
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Author : Wojciech S. Ożański
language : en
Publisher: Springer Nature
Release Date : 2019-09-16
The Partial Regularity Theory Of Caffarelli Kohn And Nirenberg And Its Sharpness written by Wojciech S. Ożański and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-16 with Mathematics categories.
This monograph focuses on the partial regularity theorem, as developed by Caffarelli, Kohn, and Nirenberg (CKN), and offers a proof of the upper bound on the Hausdorff dimension of the singular set of weak solutions of the Navier-Stokes inequality, while also providing a clear and insightful presentation of Scheffer’s constructions showing their bound cannot be improved. A short, complete, and self-contained proof of CKN is presented in the second chapter, allowing the remainder of the book to be fully dedicated to a topic of central importance: the sharpness result of Scheffer. Chapters three and four contain a highly readable proof of this result, featuring new improvements as well. Researchers in mathematical fluid mechanics, as well as those working in partial differential equations more generally, will find this monograph invaluable.
Mathematics For Nonlinear Phenomena Analysis And Computation
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Author : Yasunori Maekawa
language : en
Publisher: Springer
Release Date : 2017-11-01
Mathematics For Nonlinear Phenomena Analysis And Computation written by Yasunori Maekawa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-01 with Mathematics categories.
This volume covers some of the most seminal research in the areas of mathematical analysis and numerical computation for nonlinear phenomena. Collected from the international conference held in honor of Professor Yoshikazu Giga’s 60th birthday, the featured research papers and survey articles discuss partial differential equations related to fluid mechanics, electromagnetism, surface diffusion, and evolving interfaces. Specific focus is placed on topics such as the solvability of the Navier-Stokes equations and the regularity, stability, and symmetry of their solutions, analysis of a living fluid, stochastic effects and numerics for Maxwell’s equations, nonlinear heat equations in critical spaces, viscosity solutions describing various kinds of interfaces, numerics for evolving interfaces, and a hyperbolic obstacle problem. Also included in this volume are an introduction of Yoshikazu Giga’s extensive academic career and a long list of his published work. Students and researchers in mathematical analysis and computation will find interest in this volume on theoretical study for nonlinear phenomena.
Mathematical Analysis Of The Navier Stokes Equations
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Author : Matthias Hieber
language : en
Publisher: Springer Nature
Release Date : 2020-04-28
Mathematical Analysis Of The Navier Stokes Equations written by Matthias Hieber and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-28 with Mathematics categories.
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.
The Three Dimensional Navier Stokes Equations
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Author : James C. Robinson
language : en
Publisher: Cambridge University Press
Release Date : 2016-09-07
The Three Dimensional Navier Stokes Equations written by James C. Robinson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-07 with Mathematics categories.
An accessible treatment of the main results in the mathematical theory of the Navier-Stokes equations, primarily aimed at graduate students.
The Navier Stokes Problem In The 21st Century
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Author : Pierre Gilles Lemarie-Rieusset
language : en
Publisher: CRC Press
Release Date : 2016-04-06
The Navier Stokes Problem In The 21st Century written by Pierre Gilles Lemarie-Rieusset and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-06 with Mathematics categories.
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.
The Navier Stokes Equations Theory And Numerical Methods
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Author : John G. Heywood
language : en
Publisher: Springer
Release Date : 2006-11-14
The Navier Stokes Equations Theory And Numerical Methods written by John G. Heywood and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
These proceedings contain original (refereed) research articles by specialists from many countries, on a wide variety of aspects of Navier-Stokes equations. Additionally, 2 survey articles intended for a general readership are included: one surveys the present state of the subject via open problems, and the other deals with the interplay between theory and numerical analysis.