Renormalized solutions for the Maxwell--Stefan system with an application to uniqueness of weak solutions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914862949466112 |
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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 |