Optimal higher derivative estimates for Stokes equations with closely spaced rigid inclusions
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929627377696768 |
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| author | Dong, Hongjie Li, Haigang Teng, Huaijun Zhang, Peihao |
| author_facet | Dong, Hongjie Li, Haigang Teng, Huaijun Zhang, Peihao |
| contents | In this paper, we study the interaction between two closely spaced rigid inclusions suspended in a Stokes flow. It is well known that the stress significantly amplifies in the narrow region between the inclusions as the distance between them approaches zero. To gain deeper insight into these interactions, we derive high-order derivative estimates for the Stokes equation in the presence of two rigid inclusions in two dimensions. Our approach resonates with the method used to handle the incompressibility constraint in the standard convex integration scheme. Under certain symmetric assumptions on the domain, these estimates are shown to be optimal. As a result, we establish the precise blow-up rates of the Cauchy stress and its higher-order derivatives in the narrow region. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09135 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal higher derivative estimates for Stokes equations with closely spaced rigid inclusions Dong, Hongjie Li, Haigang Teng, Huaijun Zhang, Peihao Analysis of PDEs In this paper, we study the interaction between two closely spaced rigid inclusions suspended in a Stokes flow. It is well known that the stress significantly amplifies in the narrow region between the inclusions as the distance between them approaches zero. To gain deeper insight into these interactions, we derive high-order derivative estimates for the Stokes equation in the presence of two rigid inclusions in two dimensions. Our approach resonates with the method used to handle the incompressibility constraint in the standard convex integration scheme. Under certain symmetric assumptions on the domain, these estimates are shown to be optimal. As a result, we establish the precise blow-up rates of the Cauchy stress and its higher-order derivatives in the narrow region. |
| title | Optimal higher derivative estimates for Stokes equations with closely spaced rigid inclusions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.09135 |