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We analyze the shock formation process for the 3d non-isentropic Eulerequations with the ideal gas law, in which sounds waves interact with entropywaves to produce vorticity. Building on our theory for isentropic flows in[3,4], we give a constructive proof of shock formation from smooth initialdata. Specifically, we prove that there exist smooth solutions to thenon-isentropic Euler equations which form a generic stable shock withexplicitly computable blowup time, location, and direction. This is achieved byestablishing the asymptotic stability of a generic shock profile in modulatedself-similar variables, controlling the interaction of wave families via: (i)pointwise bounds along Lagrangian trajectories, (ii) geometric vorticitystructure, and (iii) high-order energy estimates in Sobolev spaces.

Shock formation and vorticity creation for 3d Euler