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Dispersive stabilization
for phase transitions
Federico Cacciafesta, Marta Strani and Benjamin Texier |
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Vol. 3 (2021), No. 4, 765–788
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Abstract |
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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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Keywords
Euler equations, dispersive regularization, van der Waals
pressure
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Mathematical Subject Classification
Primary: 35Q31, 35Q55, 76N10
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Milestones
Received: 3 February 2021
Revised: 31 May 2021
Accepted: 21 August 2021
Published: 12 February 2022
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Authors |
| Federico Cacciafesta | |
| Dipartimento di Matematica Università degli studi di Padova Padova Italy |
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| Marta Strani | |
| Dipartimento di Scienze Molecolari e
Nanosistemi Università Ca’ Foscari Venice Italy |
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| Benjamin Texier | |
| Institut Camille Jordan, UMR CNRS
5208 Villeurbanne France |
Université Claude Bernard Lyon France |
