Lectures on Navier-Stokes equations
By: Tsai, Tai-Peng.
Series: Graduate studies in mathematics. ; no.192.Publisher: Providence American Mathematical Society 2018Description: xii, 224p.ISBN: 9781470430962.Subject(s): Fluid dynamics | Incompressible viscous fluids | Navier-Stokes equationsDDC classification: 515.3530153205 | T782l 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 $L^3$ 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.| Item type | Current location | Collection | Call number | Status | Date due | Barcode | Item holds |
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Books
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PK Kelkar Library, IIT Kanpur | On Display | 515.3530153205 T782l (Browse shelf) | Available | A186690 |
Browsing PK Kelkar Library, IIT Kanpur Shelves , Collection code: On Display Close shelf browser
| 515.353 G131i2 An introduction to the mathematical theory of the Navier-Stokes equations [2nd ed.] | 515.353 L968n Navier–Stokes equations | 515.3530153205 T782l Lectures on Navier-Stokes equations | 515.3533 N28d Direct methods in the theory of elliptic equations | 515.782 L554f A first course in fractional Sobolev spaces | 515.782 L554f2 A first course in Sobolev spaces [2nd ed.] |
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 $L^3$ 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.
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