Shock formation and vorticity creation for compressible Euler

Vlad Vicol
Courant Institute of Mathematical Sciences, New York University
Thursday, December 3, 2020 - 3:30pm to 4:30pm
Via Zoom ID 91514486597 (contact faculty for pw)

We discuss the formation of singularities (shocks) for the compressible Euler equations with the ideal gas law. We provide a constructive proof of stable shock formation from smooth initial datum, of finite energy, and with no vacuum regions. Via modulated self-similar variables, the blow-up time and location can be explicitly computed, the geometry of the shock set can be understood, and at the blow-up time the solutions can be shown to have precisely Holder 1/3 regularity. Additionally, for the non-isentropic problem we show that sound waves interact with entropy waves to produce vorticity at the shock. This talk is based on joint work with Tristan Buckmaster and Steve Shkoller.