Prandtl Equations and Related Boundary Layer Equations

By: Yuming Qin, Xiaolei Dong, Xiuqing Wang

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Hardcover | 10 January 2025

At a Glance

Hardcover
384 Pages

Dimensions(cm)
23.39 x 15.6 x 2.24

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This book aims to present some recent results on Prandtl equations and MHD boundary layer equations.

This book is essentially divided into two parts. Chapter 1 as the first part systematically surveys the results till 2020 on Prandtl equations and MHD boundary layer equations. Chapter 2 to 6 are the main part of the book, which presents the local or/and the global wellposedness of solutions to the 2D or/and 3D Prandtl equations or/and MHD boundary layer equations. In detail, Chapter 2 is concerned with global well-posedness of solutions to the 2D Prandtl-Hartmann equations in an analytic framework. Chapter 3 investigates the local existence of solutions to the 2D Prandtl equations in a weighted Sobolev space. Chapter 4 studies the local well-posedness of solutions to the 2D mixed Prandtl equations in a Sobolev space without monotonicity and lower bound. Chapter 5 is concerned with global existence of solutions to the 2D magnetic Prandtl equations in the Prandtl-Hartmann regime. Chapter 6 proves the global existence of solutions to the 3D Prandtl equations with a special structure.

Mathematicians and physicists who are interested in fluid dynamics will find this book helpful.

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