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.

Intro
Compressible Euler Equations on Rd
D Compressible Isentropic Euler
Shock formation in 1D Burgers
Stable shock formation for 1D Euler
Finite-time breakdown of smooth solutions
D Shock formation, collision, and bounce back
Shock formation results for Euler in 2D and 3D
Simple plane wave
The method of Christodoulou
Shock formation for Euler with vorticity
2D Shock Formation
Azimuthal shocks: a showcase for the new approach
Specific vorticity evolution
New Variables for Euler
Generic shock profile in multiple space dimensions
Stable shock formation for compressible Euler
Some geometric difficulties in higher dimensions
3D compressible Euler: rotation and translation
Modulated self-similar Riemann-type Variables
Asymptotically self-similar blowup
3D Euler in Modulated Self-Similar Variables
Trajectory estimates are key Toy Model in physical variables
Some ideas of the proof