03730nam a22005295i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001700172072001600189072002300205072001500228100008100243245012800324250001800452264007200470300003200542336002600574337002600600338003600626347002400662505065700686520117901343650002602522650003402548650002802582650002402610650002602634650001902660650004402679650002802723650002402751700008302775700008302858710003402941773002602975776003603001776003603037776003603073856004603109912001403155912001403169999001703183978-981-97-4565-4DE-He21320251030114607.0cr nn 008mamaa241207s2024    si |    s    |||| 0|eng d  a97898197456549978-981-97-4565-47 a10.1007/978-981-97-4565-42doi 4aQC19.2-20.85 7aPHU2bicssc 7aSCI0400002bisacsh 7aPHU2thema1 aQin, Yuming.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98865610aPrandtl Equations and Related Boundary Layer Equationsh[electronic resource] /cby Yuming Qin, Xiaolei Dong, Xiuqing Wang.  a1st ed. 2024. 1aSingapore :bSpringer Nature Singapore :bImprint: Springer,c2024.  aX, 373 p.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 aPreface -- 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.  aThis 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. 0aMathematical physics. 0aSoft condensed matter.966723 0aDifferential equations. 0aIntegral equations.14aMathematical Physics.24aFluids.96754024aMathematical Methods in Physics.97087724aDifferential Equations.24aIntegral Equations.1 aDong, Xiaolei.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9886571 aWang, Xiuqing.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9886582 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978981974564708iPrinted edition:z978981974566108iPrinted edition:z978981974567840uhttps://doi.org/10.1007/978-981-97-4565-4  aZDB-2-PHA  aZDB-2-SXP  c65553d65553