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Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations by Simon Markfelder is a nonfiction available to read on EtoBox.

What is Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations about?

This book applies the convex integration method to multi-dimensional compressible Euler equations in the barotropic case as well as the full system with temperature. The convex integration technique, originally developed in the context of differential inclusions, was applied in the groundbreaking work of De Lellis and Székelyhidi to the incompressible Euler equations, leading to infinitely many solutions. This theory was later refined to prove non-uniqueness of solutions of the compressible Euler system, too. These non-uniqueness results all use an ansatz which reduces the equations to a kind of incompressible system to which a slight modification of the incompressible theory can be applied. This book presents, for the first time, a generalization of the De Lellis–Székelyhidi approach to the setting of compressible Euler equations.The structure of this book is as follows: after providing an accessible introduction to the subject, including the essentials of hyperbolic conservation laws, the idea of convex integration in the compressible framework is developed. The main result proves that under a certain assumption there exist infinitely many solutions to an abstract initial boundar

Who reads Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations?

Author

Simon Markfelder

Publisher

Springer International Publishing : Imprint: Springer

Published

2021

Language

EN

ISBN

9783030837846

Category

nonfiction

Subjects

Mathematics, Science, Physics