Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations (Paperback, 1st ed. 2021)

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 Szekelyhidi 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-Szekelyhidi 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 boundary value problem for the Euler system. Next some applications of this theorem are discussed, in particular concerning the Riemann problem. Finally there is a survey of some related results. This self-contained book is suitable for both beginners in the field of hyperbolic conservation laws as well as for advanced readers who already know about convex integration in the incompressible framework.

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	Lecture Notes in Mathematics, 2294
Release date:	October 2021
First published:	2021
Authors:	Simon Markfelder
Dimensions:	235 x 155mm (L x W)
Format:	Paperback
Pages:	242
Edition:	1st ed. 2021
ISBN-13:	978-3-03-083784-6
Categories:	Books > Science & Mathematics > Mathematics > Numerical analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis Books > Science & Mathematics > Physics > Classical mechanics > General
LSN:	3-03-083784-X
Barcode:	9783030837846

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