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Uniqueness of shock waves under small perturbations for the Isentropic Euler Equations

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FKT - Frontiers in kinetic theory: connecting microscopic to macroscopic scales - KineCon 2022

We consider bounded entropy solutions of the isentropic Euler equations with gamma = 3. We use the kinetic formulation of the equations and a De Giorgi type argument to show weak solutions of this type possess some a priori regularity. Combined with the relative entropy method, we are able to show uniqueness for small shocks under small perturbations, but without any regularity assumptions on the perturbation. This result provides a limit on the possible types of solutions constructible by convex integration techniques

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