Existence and regularity of the pressure for the stochastic Navier-Stokes equations

We prove, on one hand, that for a convenient body force with values in the distribution space (H−1(D))d, where D is the geometric domain of the fluid, there exist a velocity u and a pressure p solution of the stochastic Navier-Stokes equation in dimension 2, 3 or 4. On the other hand, we prove that,...

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Detalles Bibliográficos
Autores: Langa Rosado, José Antonio, Real Anguas, José, Simon, Jacques
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2003
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/47178
Acceso en línea:http://hdl.handle.net/11441/47178
https://doi.org/10.1007/s00245-003-0773-7
Access Level:acceso abierto
Palabra clave:Stochastic
Navier-Stokes equations
Pressure
Descripción
Sumario:We prove, on one hand, that for a convenient body force with values in the distribution space (H−1(D))d, where D is the geometric domain of the fluid, there exist a velocity u and a pressure p solution of the stochastic Navier-Stokes equation in dimension 2, 3 or 4. On the other hand, we prove that, for a body force with values in the dual space V0 of the divergence free subspace V of (H1 0(D))d, in general it is not possible to solve the stochastic Navier-Stokes equations. More precisely, although such body forces have been considered, there is no topological space in which Navier-Stokes equations could be meaningful for them.