Stress concentration between two adjacent rigid particles in Navier-Stokes flow
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913585255415808 |
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| author | Li, Haigang Zhang, Peihao |
| author_facet | Li, Haigang Zhang, Peihao |
| contents | In this paper we investigate the stress concentration problem that occurs when two convex rigid particles are closely immersed in a fluid flow. The governing equations for the fluid flow are the stationary incompressible Navier-Stokes equations. We establish precise upper bounds for the gradients and second-order derivatives of the fluid velocity as the distance between particles approaches zero, in dimensions two and three. The optimality of these blow-up rates of the gradients is demonstrated by deriving corresponding lower bounds. New difficulties arising from the nonlinear term in the Navier-Stokes equations is overcome. Consequently, the blow up rates of the Cauchy stress are studied as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16413 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stress concentration between two adjacent rigid particles in Navier-Stokes flow Li, Haigang Zhang, Peihao Analysis of PDEs In this paper we investigate the stress concentration problem that occurs when two convex rigid particles are closely immersed in a fluid flow. The governing equations for the fluid flow are the stationary incompressible Navier-Stokes equations. We establish precise upper bounds for the gradients and second-order derivatives of the fluid velocity as the distance between particles approaches zero, in dimensions two and three. The optimality of these blow-up rates of the gradients is demonstrated by deriving corresponding lower bounds. New difficulties arising from the nonlinear term in the Navier-Stokes equations is overcome. Consequently, the blow up rates of the Cauchy stress are studied as well. |
| title | Stress concentration between two adjacent rigid particles in Navier-Stokes flow |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.16413 |