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arXiv · 2501.02915

Extending relative entropy for Korteweg-Type models with non-monotone pressure:large friction limit and weak-strong uniqueness

Giada Cianfarani Carnevale·Jan Giesselmann
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Abstract

In this paper we study weak-strong uniqueness and singular relaxation limits for the Euler--Korteweg and Navier--Stokes--Korteweg systems with non monotone pressure. Both weak-strong uniqueness and the relaxation limit are investigated using relative entropy technique. We make use of the enlarged formulation of the model in terms of the drift velocity introduced in [6], generalizing in this way results proved in [17] for the Euler-Korteweg model, by allowing more general capillarity functions, and the result contained in [8] for the monotone pressure case.

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Giada Cianfarani Carnevale, Jan Giesselmann. 2025-01-06. Extending relative entropy for Korteweg-Type models with non-monotone pressure:large friction limit and weak-strong uniqueness. https://arxiv.org/abs/2501.02915

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