{"product_id":"the-mathematical-analysis-of-the-incompressible-euler-and-navier-stokes-equations-an-introduction-paperback-softback-9781470471781","title":"The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations; An Introduction (Paperback \/ softback) 9781470471781","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eAn Introduction\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJacob Bedrossian (Author), Vlad Vicol (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781470471781\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 30 December 2022\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e218 pages\u003cbr\u003e25.7 x 17.9 x 1.8 cm, 0.452 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe aim of this book is to provide beginning graduate students who completed the first two semesters of graduate-level analysis and PDE courses with a first exposure to the mathematical analysis of the incompressible Euler and Navier-Stokes equations. The book gives a concise introduction to the fundamental results in the well-posedness theory of these PDEs, leaving aside some of the technical challenges presented by bounded domains or by intricate functional spaces.\u003cbr\u003e\u003cbr\u003eChapters 1 and 2 cover the fundamentals of the Euler theory: derivation, Eulerian and Lagrangian perspectives, vorticity, special solutions, existence theory for smooth solutions, and blowup criteria. Chapters 3, 4, and 5 cover the fundamentals of the Navier-Stokes theory: derivation, special solutions, existence theory for strong solutions, Leray theory of weak solutions, weak-strong uniqueness, existence theory of mild solutions, and Prodi-Serrin regularity criteria. Chapter 6 provides a short guide to the must-read topics, including active research directions, for an advanced graduate student working in incompressible fluids. It may be used as a roadmap for a topics course in a subsequent semester. The appendix recalls basic results from real, harmonic, and functional analysis. Each chapter concludes with exercises, making the text suitable for a one-semester graduate course.\u003cbr\u003e\u003cbr\u003ePrerequisites to this book are the first two semesters of graduate-level analysis and PDE courses.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cul\u003e\n\u003cli\u003eIdeal incompressible fluids: The Euler equations\u003c\/li\u003e\n\u003cli\u003eExistence of solutions and continuation criteria for Euler\u003c\/li\u003e\n\u003cli\u003eIncompressible viscous fluids: The Navier-Stokes equations\u003c\/li\u003e\n\u003cli\u003eLeray-Hopf weak solutions of Navier-Stokes\u003c\/li\u003e\n\u003cli\u003eMild solutions of Navier-Stokes\u003c\/li\u003e\n\u003cli\u003eA survey of some advanced topics\u003c\/li\u003e\n\u003cli\u003eAppendix\u003c\/li\u003e\n\u003cli\u003eBibliography\u003c\/li\u003e\n\u003cli\u003eIndex\u003c\/li\u003e\n\u003c\/ul\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003c\/font\u003e","brand":"American Mathematical Society","offers":[{"title":"Brand New","offer_id":52681337733400,"sku":"9781470471781","price":71.39,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/freshlyprintedbooks.co.uk\/products\/the-mathematical-analysis-of-the-incompressible-euler-and-navier-stokes-equations-an-introduction-paperback-softback-9781470471781","provider":"Freshly Printed Books","version":"1.0","type":"link"}