Shock Formation and Vorticity Creation for Compressible Euler
Explore a comprehensive seminar on shock formation and vorticity creation in compressible Euler equations. Delve into the long-term project by Vlad Vicol, Tristan Buckmaster, and Steve Shkoller, focusing on singularity formation in compressible Euler equations with ideal gas law. Learn about constructive proof of stable shock formation from smooth initial data, finite energy, and no vacuum regions. Discover how modulated self-similar variables enable explicit computation of blow-up time and location, resulting in Holder 1/3 regularity at blow-up. Examine the interaction between sound waves and entropy waves in non-isentropic problems, leading to vorticity production at shocks. Gain insights into various aspects of the research, including 1D Burgers equations, finite-time breakdown of smooth solutions, shock formation in multiple dimensions, and the method of Christodoulou. Explore new variables for Euler equations, generic shock profiles, and the challenges of higher dimensions. Understand the importance of trajectory estimates and the use of modulated self-similar Riemann-type variables in analyzing 3D compressible Euler equations. Read more