Special Session 2: New frontiers in the compressible mathematical fluid mechanics and thermodynamics

Various approaches to the issue of existence for systems of compressible flows
Piotr B Mucha
University of Warsaw
Poland
Co-Author(s):    
Abstract:
In this talk, I will discuss several currently available techniques for proving the existence of weak solutions to systems describing compressible flows. The presentation will focus on methods based on the construction of solutions, with particular emphasis on their main ideas, limitations, and the open problems that remain in the field. Special attention will be given to approaches relying on the renormalization of the continuity equation. Methods based on convex integration will not be considered. The aim of the talk is to provide a comparative overview of existing analytical frameworks and to highlight directions for future research in the mathematical theory of compressible fluid models.