Screen LibraryLectures on Navier-Stokes equations /
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 th...
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| Main Authors: | |
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| Published: |
American Mathematical Society,
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| Publisher Address: | Providence, Rhode Island : |
| Publication Dates: | [2018] |
| Literature type: | Book |
| Language: | English |
| Series: |
Graduate studies in mathematics ; volume 192. |
| Subjects: | |
| Summary: |
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-Sverak 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. |
| Carrier Form: | xii, 224 pages ; 27 cm. |
| Bibliography: | Includes bibliographical references (pages 211-222) and index. |
| ISBN: |
9781470430962 1470430967 |
| Index Number: | QA911 |
| CLC: |
O35 O175.2 |
| Call Number: | O175.2/T877 |
| Contents: | Ch. 1. Introduction -- Ch. 2. Steady states -- Ch. 3. Weak solutions -- Ch. 4. Strong solutions -- Ch. 5. Mild solutions -- Ch. 6. Partial regularity -- Ch. 7. Boundary value problem and bifurcation -- Ch. 8. Self-similar solutions -- Ch. 9. The uniform L³ class -- Ch. 10. Axisymmetric flows. |