Shock Formation and Vorticity Creation for 3d Euler

We analyze the shock formation process for 3D nonisentropic Euler equations with ideal gas law, in which sound waves interact entropy to produce vorticity. Building on our theory isentropic flows [3, 4], we give a constructive proof of from smooth initial data. Specifically, prove that there exist solutions form generic stable explicitly computable blowup time, location, and direction. This is achieved by establishing asymptotic stability profile modulated self-similar variables, controlling interaction wave families via: (i) pointwise bounds along Lagrangian trajectories, (ii) geometric vorticity structure, (iii) high-order energy estimates Sobolev spaces. © 2022 Wiley Periodicals LLC.