Simon Markfelder
Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations
Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations
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Excellent- More about Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations
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. It proves that under a certain assumption, there exist infinitely many solutions to an abstract initial boundary value problem for the Euler system, and discusses applications to the Riemann problem. It is suitable for beginners and advanced readers.
Format: Paperback / softback
Length: 242 pages
Publication date: 21 October 2021
Publisher: Springer Nature Switzerland AG
This book delves into the realm of multi-dimensional compressible Euler equations, employing the convex integration method. Initially developed for differential inclusions, it was later applied by De Lellis and Székelyhidi to the incompressible Euler equations, yielding an abundance of solutions. This theory was further refined to establish the non-uniqueness of solutions for the compressible Euler system. These non-uniqueness results are derived through an ansatz that transforms the equations into a form resembling an incompressible system, which can be adapted with slight modifications from the incompressible theory.
This book presents a groundbreaking extension of the De Lellis–Székelyhidi approach to the realm of compressible Euler equations. It begins with an accessible introduction to the subject, encompassing the fundamentals of hyperbolic conservation laws. The core result establishes the existence of infinitely many solutions to an abstract initial boundary value problem for the Euler system, under a specific assumption. Subsequent applications of this theorem are explored, particularly in relation to the Riemann problem. Finally, a comprehensive survey of related results is provided. This self-contained book caters to both novice enthusiasts in hyperbolic conservation laws and advanced readers familiar with convex integration in the incompressible framework.
Weight: 391g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030837846
Edition number: 1st ed. 2021
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