Shock formation for the 3d Euler equations

Friday, March 19, 2021 - 3:00pm
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.

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