The Euler equations with variable coefficients
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914015327813632 |
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| author | Ingimarson, Benjamin Kukavica, Igor Tuffaha, Amjad |
| author_facet | Ingimarson, Benjamin Kukavica, Igor Tuffaha, Amjad |
| contents | We establish local-in-time existence for the Euler equations on a bounded domain with space-time dependent variable coefficients, given initial data $v_0 \in H^r$ under the optimal regularity condition $r > 2.5$. In the case $r = 3$, we further prove a Beale-Kato-Majda criterion that relates blow-up in the $H^r$ norm to the BMO norm of the variable vorticity $ζ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01067 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Euler equations with variable coefficients Ingimarson, Benjamin Kukavica, Igor Tuffaha, Amjad Analysis of PDEs We establish local-in-time existence for the Euler equations on a bounded domain with space-time dependent variable coefficients, given initial data $v_0 \in H^r$ under the optimal regularity condition $r > 2.5$. In the case $r = 3$, we further prove a Beale-Kato-Majda criterion that relates blow-up in the $H^r$ norm to the BMO norm of the variable vorticity $ζ$. |
| title | The Euler equations with variable coefficients |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.01067 |