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Main Authors: Bresch, Didier, Lacave, Christophe, Szlenk, Maja
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2601.19442
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author Bresch, Didier
Lacave, Christophe
Szlenk, Maja
author_facet Bresch, Didier
Lacave, Christophe
Szlenk, Maja
contents The main objective of this paper is to prove that if capillarity effect is taken into account then there exist dissipative solutions to a system describing viscoplastic compressible flows with density dependent viscosities in a periodic domain $\T^d$ with $d=2,3$. We calculate the relative entropy inequality and in consequence show existence of dissipative solutions and the weak-strong uniqueness for this system. Our result extends the recent result concerning the link between Euler--Korteweg and Navier--Stokes--Korteweg systems for Newtonian flows (when the viscosity depends on the density) [See D.~Bresch, M. Gisclon, I. Lacroix-Violet, {\it Arch. Rational Mech. Anal.} (2019)] to non-Newtonian flows.
format Preprint
id arxiv_https___arxiv_org_abs_2601_19442
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Dissipative Solutions to a Compressible Non-Newtonian Korteweg System with Density-Dependent Viscous Stress Tensor
Bresch, Didier
Lacave, Christophe
Szlenk, Maja
Analysis of PDEs
The main objective of this paper is to prove that if capillarity effect is taken into account then there exist dissipative solutions to a system describing viscoplastic compressible flows with density dependent viscosities in a periodic domain $\T^d$ with $d=2,3$. We calculate the relative entropy inequality and in consequence show existence of dissipative solutions and the weak-strong uniqueness for this system. Our result extends the recent result concerning the link between Euler--Korteweg and Navier--Stokes--Korteweg systems for Newtonian flows (when the viscosity depends on the density) [See D.~Bresch, M. Gisclon, I. Lacroix-Violet, {\it Arch. Rational Mech. Anal.} (2019)] to non-Newtonian flows.
title Dissipative Solutions to a Compressible Non-Newtonian Korteweg System with Density-Dependent Viscous Stress Tensor
topic Analysis of PDEs
url https://arxiv.org/abs/2601.19442