Extending relative entropy for Korteweg-Type models with non-monotone pressure:large friction limit and weak-strong uniqueness
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912577230995456 |
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| author | Carnevale, Giada Cianfarani Giesselmann, Jan |
| author_facet | Carnevale, Giada Cianfarani Giesselmann, Jan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02915 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extending relative entropy for Korteweg-Type models with non-monotone pressure:large friction limit and weak-strong uniqueness Carnevale, Giada Cianfarani Giesselmann, Jan Analysis of PDEs 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. |
| title | Extending relative entropy for Korteweg-Type models with non-monotone pressure:large friction limit and weak-strong uniqueness |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.02915 |