Spatial $C^1$, $C^2$, and Schauder estimates for nonstationary Stokes equations with Dini mean oscillation coefficients
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918215267909632 |
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| author | Dong, Hongjie Kwon, Hyunwoo |
| author_facet | Dong, Hongjie Kwon, Hyunwoo |
| contents | We establish the spatial differentiability of weak solutions to nonstationary Stokes equations in divergence form with variable viscosity coefficients having $L_2$-Dini mean oscillations. As a corollary, we derive local spatial Schauder estimates for such equations if the viscosity coefficient belongs to $C^α_x$. Similar results also hold for strong solutions to nonstationary Stokes equations in nondivergence form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20125 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spatial $C^1$, $C^2$, and Schauder estimates for nonstationary Stokes equations with Dini mean oscillation coefficients Dong, Hongjie Kwon, Hyunwoo Analysis of PDEs 76D07, 35B45, 35B65, 35Q35 We establish the spatial differentiability of weak solutions to nonstationary Stokes equations in divergence form with variable viscosity coefficients having $L_2$-Dini mean oscillations. As a corollary, we derive local spatial Schauder estimates for such equations if the viscosity coefficient belongs to $C^α_x$. Similar results also hold for strong solutions to nonstationary Stokes equations in nondivergence form. |
| title | Spatial $C^1$, $C^2$, and Schauder estimates for nonstationary Stokes equations with Dini mean oscillation coefficients |
| topic | Analysis of PDEs 76D07, 35B45, 35B65, 35Q35 |
| url | https://arxiv.org/abs/2412.20125 |