The Stokes problem with Navier boundary conditions in irregular domains
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866909486080327680 |
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| author | Breit, Dominic Schwarzacher, Sebastian |
| author_facet | Breit, Dominic Schwarzacher, Sebastian |
| contents | We consider the steady Stokes equations supplemented with Navier boundary conditions including a non-negative friction coefficient. We prove maximal regularity estimates (including the prominent spaces $W^{1,p}$ and $W^{2,p}$ for $1<p<\infty$ for the velocity field) in bounded domains of minimal regularity. Interestingly, exactly one derivative more is required for the local boundary charts compared to the case of no-slip boundary conditions. We demonstrate the sharpness of our results by a propos examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06433 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Stokes problem with Navier boundary conditions in irregular domains Breit, Dominic Schwarzacher, Sebastian Analysis of PDEs We consider the steady Stokes equations supplemented with Navier boundary conditions including a non-negative friction coefficient. We prove maximal regularity estimates (including the prominent spaces $W^{1,p}$ and $W^{2,p}$ for $1<p<\infty$ for the velocity field) in bounded domains of minimal regularity. Interestingly, exactly one derivative more is required for the local boundary charts compared to the case of no-slip boundary conditions. We demonstrate the sharpness of our results by a propos examples. |
| title | The Stokes problem with Navier boundary conditions in irregular domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.06433 |