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Shock Formation and Vorticity Creation for 3d Euler
Authors:Tristan Buckmaster  Steve Shkoller  Vlad Vicol
Institution:1. Department of Mathematics, Princeton University, Princeton, NJ, 08544 USA;2. Department of Mathematics, UC Davis, Davis, CA, 95616 USA;3. Courant Institute, New York University, New York, NY, 10012 USA
Abstract: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. © 2022 Wiley Periodicals LLC.
Keywords:
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