Dispersive regularization for phase transitions

Federico Cacciafesta; Marta Strani; Benjamin Texier

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arXiv · 2102.01457

Dispersive regularization for phase transitions

Federico Cacciafesta·Marta Strani·Benjamin Texier

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Abstract

We introduce a dispersive regularization of 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 regularization is of Schroedinger type. In particular, the regularized system is complex-valued. It has a conservation law, which, for real unknowns, is identical to the energy of the unregularized physical system. The regularized system supports high-frequency solutions, with an existence time or an amplitude which depend strongly on the pressure law.

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Federico Cacciafesta, Marta Strani, Benjamin Texier. 2021-02-02. Dispersive regularization for phase transitions. https://arxiv.org/abs/2102.01457

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