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...

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Detalles Bibliográficos
Autores: Bello Jiménez, Juan Antonio, Fernández Cara, Enrique, Lemoine, Jérôme, Simon, Jacques
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
Descripción
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.