Vol. 3, No. 4, 2021

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Dispersive stabilization for phase transitions

Federico Cacciafesta, Marta Strani and Benjamin Texier

Vol. 3 (2021), No. 4, 765–788

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.

Euler equations, dispersive regularization, van der Waals pressure
Mathematical Subject Classification
Primary: 35Q31, 35Q55, 76N10
Received: 3 February 2021
Revised: 31 May 2021
Accepted: 21 August 2021
Published: 12 February 2022
Federico Cacciafesta
Dipartimento di Matematica
Università degli studi di Padova
Marta Strani
Dipartimento di Scienze Molecolari e Nanosistemi
Università Ca’ Foscari
Benjamin Texier
Institut Camille Jordan, UMR CNRS 5208
Université Claude Bernard