Abstract

We study the effects of dispersive stabilization on the compressible Euler equations in Lagrangian coordinates in the one-dimensional torus. We assume a van der Waals pressure law, which presents both hyperbolic and elliptic zones. The dispersive stabilization term is of Schrödinger type. In particular, the stabilized system is complex-valued. It has a conservation law, which, for real unknowns, is identical to the energy of the original physical system. The stabilized system supports high-frequency solutions, with an existence time or an amplitude which depend strongly on the pressure law.

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