Shock Formation and Vorticity Creation for 3d Euler

We analyze the shock formation process for the 3D nonisentropic Euler equations with the ideal gas law, in which sound waves interact with entropy waves to produce vorticity. Building on our theory for isentropic flows in [3, 4], we give a constructive proof of shock formation from smooth initial data. Specifically, we prove that there exist smooth solutions to the nonisentropic Euler equations which form a generic stable shock with explicitly computable blowup time, location, and direction. This is achieved by establishing 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. (c) 2022 Wiley Periodicals LLC.

Automated summary

We analyze the formation process of shocks in the 3D nonisentropic Euler equations with the ideal gas law, where sound waves interact with entropy waves to produce vorticity. Building on previous theories, we provide a constructive proof of shock formation from smooth initial data. We prove the existence of smooth solutions to the nonisentropic Euler equations that form a stable shock with computable blowup time, location, and direction by establishing the asymptotic stability of a generic shock profile in modulated self-similar variables and controlling the interaction of wave families through various techniques.