Solvability and Ill Posedness of the Isentropic Euler System

Explore the intriguing aspects of solvability and ill-posedness in the isentropic Euler system through this 53-minute lecture by Martina Hofmanová, presented as part of the Hausdorff Junior Trimester Program on Randomness, PDEs and Nonlinear Fluctuations. Delve into the application of convex integration methods for constructing infinite wild solutions and surprising approximation results. Examine the contrasting approach using Markov selections and a novel concept of dissipative solutions, which enables the selection of physically reasonable solution semiflow and the exclusion of oscillation defects in specific cases. Gain insights into the complex nature of this mathematical system and its implications for fluid dynamics and related fields.