Renormalized solutions for the Maxwell--Stefan system with an application to uniqueness of weak solutions

Fuente: arXiv
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Hauptverfasser: Georgiadis, Stefanos, Kim, Hoyoun, Tzavaras, Athanasios E.
Format: Preprint
Veröffentlicht: 2023
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author Georgiadis, Stefanos
Kim, Hoyoun
Tzavaras, Athanasios E.
author_facet Georgiadis, Stefanos
Kim, Hoyoun
Tzavaras, Athanasios E.
contents We give conditions that guarantee uniqueness of renormalized solutions for the Maxwell-Stefan system. The proof is based on an identity for the evolution of the symmetrized relative entropy. Using the method of doubling the variables we derive the identity for two renormalized solutions and use information on the spectrum of the Maxwell-Stefan matrix to estimate the symmetrized relative entropy and show uniqueness. We then show that weak solutions for the Maxwell-Stefan system have sufficient regularity to produce renormalized solutions. Combining the two results yields a uniqueness result for weak solutions of the Maxwell-Stefan system with bounded fluxes.
format Preprint
id arxiv_https___arxiv_org_abs_2311_10465
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Renormalized solutions for the Maxwell--Stefan system with an application to uniqueness of weak solutions
Georgiadis, Stefanos
Kim, Hoyoun
Tzavaras, Athanasios E.
Analysis of PDEs
35D99, 35Q35, 76N10, 76R50, 76T30
We give conditions that guarantee uniqueness of renormalized solutions for the Maxwell-Stefan system. The proof is based on an identity for the evolution of the symmetrized relative entropy. Using the method of doubling the variables we derive the identity for two renormalized solutions and use information on the spectrum of the Maxwell-Stefan matrix to estimate the symmetrized relative entropy and show uniqueness. We then show that weak solutions for the Maxwell-Stefan system have sufficient regularity to produce renormalized solutions. Combining the two results yields a uniqueness result for weak solutions of the Maxwell-Stefan system with bounded fluxes.
title Renormalized solutions for the Maxwell--Stefan system with an application to uniqueness of weak solutions
topic Analysis of PDEs
35D99, 35Q35, 76N10, 76R50, 76T30
url https://arxiv.org/abs/2311.10465