Preface -- Chapter 1. Survey on the Prandtls Equations and Related Boundary Layer Equations -- Chapter 2. Global Well-posedness of Solutions to the 2D Prandtl-Hartmann Equations in Analytic Framework -- Chapter 3. Local Existence of Solutions to the 2D Prandtl Equations in A Weighted Sobolev Space -- Chapter 4. Local Well-posedness of Solutions to the 2D Mixed Prandtl Equations in A Sobolev Space Without Monotonicity or Lower Bound -- Chapter 5. Local Well-posedness of Solutions to 2D Magnetic Prandtl Model in the Prandtl-Hartmann regime -- Chapter 6. Local Existence of Solutions to 3D Prandtl Equations with a Special Structure -- Bibliography.

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 and the global well-posedness of solutions to the Prandtl equations 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 local 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.