On the zero capillarity limit for the Euler-Korteweg system
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909493219033088 |
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| author | Audiard, Corentin Vassenet, Marc-Antoine |
| author_facet | Audiard, Corentin Vassenet, Marc-Antoine |
| contents | We study the Euler-Korteweg equations with a weak capillarity tensor. It formally converges to the Euler equations in the zero capillarity limit. Our aim is two-fold : first we prove rigorously this limit in R d , d $\ge$ 1, and obtain a more precise BKW expansion of the solution, second we initiate the study of the problem on the half space. In this case we obtain a priori estimates for the solutions that degenerate as the capillary coefficient converges to zero, and we explain this degeneracy with the construction of a (formal) BKW expansion that exhibits boundary layers. The results on the full space extend and improve a classical result of Grenier (1998) on the semi-classical limit of nonlinear Schr{ö}dinger equations. The analysis on the half space is restricted to the case of quantum fluids with irrotational velocity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10034 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the zero capillarity limit for the Euler-Korteweg system Audiard, Corentin Vassenet, Marc-Antoine Analysis of PDEs We study the Euler-Korteweg equations with a weak capillarity tensor. It formally converges to the Euler equations in the zero capillarity limit. Our aim is two-fold : first we prove rigorously this limit in R d , d $\ge$ 1, and obtain a more precise BKW expansion of the solution, second we initiate the study of the problem on the half space. In this case we obtain a priori estimates for the solutions that degenerate as the capillary coefficient converges to zero, and we explain this degeneracy with the construction of a (formal) BKW expansion that exhibits boundary layers. The results on the full space extend and improve a classical result of Grenier (1998) on the semi-classical limit of nonlinear Schr{ö}dinger equations. The analysis on the half space is restricted to the case of quantum fluids with irrotational velocity. |
| title | On the zero capillarity limit for the Euler-Korteweg system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.10034 |