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Lecture Notes On Regularity Theory For The Navier-stokes Equations

2014-09-16 Mathematics
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Release : 2014-09-16
Genre : Mathematics
Kind : eBook
Book Rating : 423/5 ( reviews)

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Book Synopsis Lecture Notes On Regularity Theory For The Navier-stokes Equations by : Gregory Seregin

Download or read book Lecture Notes On Regularity Theory For The Navier-stokes Equations written by Gregory Seregin. This book was released on 2014-09-16. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

The Navier-Stokes Equations

2001-09-27 Mathematics
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Release : 2001-09-27
Genre : Mathematics
Kind : eBook
Book Rating : 896/5 ( reviews)

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Book Synopsis The Navier-Stokes Equations by : Rodolfo Salvi

Download or read book The Navier-Stokes Equations written by Rodolfo Salvi. This book was released on 2001-09-27. Available in PDF, EPUB and Kindle. Book excerpt: "Contains proceedings of Varenna 2000, the international conference on theory and numerical methods of the navier-Stokes equations, held in Villa Monastero in Varenna, Lecco, Italy, surveying a wide range of topics in fluid mechanics, including compressible, incompressible, and non-newtonian fluids, the free boundary problem, and hydrodynamic potential theory."

The Navier-Stokes Equations Theory and Numerical Methods

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 413/5 ( reviews)

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Book Synopsis The Navier-Stokes Equations Theory and Numerical Methods by : John G. Heywood

Download or read book The Navier-Stokes Equations Theory and Numerical Methods written by John G. Heywood. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Partial Regularity Theory of Caffarelli, Kohn, and Nirenberg and its Sharpness

2019-09-16 Mathematics
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Release : 2019-09-16
Genre : Mathematics
Kind : eBook
Book Rating : 613/5 ( reviews)

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Book Synopsis The Partial Regularity Theory of Caffarelli, Kohn, and Nirenberg and its Sharpness by : Wojciech S. Ożański

Download or read book The Partial Regularity Theory of Caffarelli, Kohn, and Nirenberg and its Sharpness written by Wojciech S. Ożański. This book was released on 2019-09-16. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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