The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations

Released on by Jacob Bedrossian
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  • The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations Book Detail

  • Author : Jacob Bedrossian
  • Release Date : 2022-09-21
  • Publisher : American Mathematical Society
  • Genre : Mathematics
  • Pages : 235
  • ISBN 13 : 1470470497
  • File Size : 94,94 MB
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The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations by Jacob Bedrossian PDF Summary

Book Description: The 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. Chapters 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. Prerequisites to this book are the first two semesters of graduate-level analysis and PDE courses.

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Topics in Applied Mathematics and Modeling

Topics in Applied Mathematics and Modeling

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