03936nam a22005775i 4500 978-981-97-4565-4 DE-He213 20251030114607.0 cr nn 008mamaa 241207s2024 si | s |||| 0|eng d 9789819745654 978-981-97-4565-4 10.1007/978-981-97-4565-4 doi QC19.2-20.85 PHU bicssc SCI040000 bisacsh PHU thema Qin, Yuming. author. aut http://id.loc.gov/vocabulary/relators/aut 88656 Prandtl Equations and Related Boundary Layer Equations [electronic resource] / by Yuming Qin, Xiaolei Dong, Xiuqing Wang. 1st ed. 2024. Singapore : Springer Nature Singapore : Imprint: Springer, 2024. X, 373 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 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. Mathematical physics. Soft condensed matter. 66723 Differential equations. Integral equations. Mathematical Physics. Fluids. 67540 Mathematical Methods in Physics. 70877 Differential Equations. Integral Equations. Dong, Xiaolei. author. aut http://id.loc.gov/vocabulary/relators/aut 88657 Wang, Xiuqing. author. aut http://id.loc.gov/vocabulary/relators/aut 88658 SpringerLink (Online service) Springer Nature eBook Printed edition: 9789819745647 Printed edition: 9789819745661 Printed edition: 9789819745678 https://doi.org/10.1007/978-981-97-4565-4 ZDB-2-PHA ZDB-2-SXP 65553 65553