Shock formation for the 3d Euler equations

Date: 
Friday, March 19, 2021 - 3:00pm
Location: 
Zoom
Speaker: 
Steve Shkoller

Abstract: In this talk, I will discuss the shock formation process for the 3d compressible Euler equations, in which sounds waves interact with entropy waves to produce vorticity. Smooth solutions form a generic stable shock with explicitly computable blowup time, location, and direction. Our method establishes the asymptotic stability of a generic shock profile in modulated self-similar variables, controlling the interaction of wave families via: (i) pointwise bounds along Lagrangian trajectories, (ii) geometric vorticity structure, and (iii) high-order energy estimates in Sobolev spaces. This is joint work with T. Buckmaster and V. Vicol.

Please access the talk through the Research Seminars page ( https://researchseminars.org/seminar/MO_Analysis ); you will need to register for a free account. If you have any difficulty, please contact Samuel Walsh (walshsa@missouri.edu).