The differentiability of the drag with respect to the variations of a Lipschitz domain in a Navier-Stokes flow
This paper is concerned with the computation of the drag T associated with a body traveling at uniform velocity in a fluid governed by the stationary Navier–Stokes equations. It is assumed that the fluid fills a domain of the form Ω+u, where Ω ⊂ R3 is a reference domain and u is a displacement field...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 1997 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/41448 |
| Acceso en línea: | http://hdl.handle.net/11441/41448 https://doi.org/10.1137/S0363012994278213 |
| Access Level: | acceso abierto |
| Palabra clave: | domain optimization hydrodynamic drag Navier–Stokes equations Lipschitz domains optimal control |
| Sumario: | This paper is concerned with the computation of the drag T associated with a body traveling at uniform velocity in a fluid governed by the stationary Navier–Stokes equations. It is assumed that the fluid fills a domain of the form Ω+u, where Ω ⊂ R3 is a reference domain and u is a displacement field. We assume only that Ω is a Lipschitz domain and that u is Lipschitz-continuous. We prove that, at least when the velocity of the body is sufficiently small, u 7→ T(Ω + u) is a C∞ mapping (in a ball centered at 0). We also compute the derivative at 0. |
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