Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations

Simon Markfelder is currently a postdoctoral researcher at the University of Cambridge, United Kingdom. He completed his PhD at the University of Wuerzburg, Germany, in 2020 under the supervision of Christian Klingenberg. Simon Markfelder has published several papers in which he applies the convex integration technique to the compressible Euler equations.

• - Part I The Problem Studied in This Book. - 1. Introduction. - 2. Hyperbolic Conservation Laws. - 3. The Euler Equations as a Hyperbolic System of Conservation Laws. - Part II Convex Integration. - 4. Preparation for Applying Convex Integration to Compressible Euler. - 5. Implementation of Convex Integration. - Part III Application to Particular Initial (Boundary) Value Problems. - 6. Infinitely Many Solutions of the Initial Boundary Value Problem for Barotropic Euler. - 7. Riemann Initial Data in Two Space Dimensions for Isentropic Euler. - 8. Riemann Initial Data in Two Space Dimensions for Full Euler.

“The book is detailed and clear, presenting the necessary technical tools and arguments in a clean and understandable manner. The material is well-organized … . The book is a comprehensive and self-contained introduction to convex integration applied to fluid dynamics, and it can be read without any particular prior knowledge of the subject. It contains the fundamental ideas with detailed proofs of the main results and various references to the literature for interested researchers.” (Stefano Bianchini, zbMATH 1546.35001, 2024)