Local strong solutions of a parabolic system related to the Boussinesq approximation for buoyancy-driven flow with viscous heating

We propose a modification of the classical Navier-Stokes-Boussinesq system of equations, which governs buoyancy-driven flows of viscous, incompressible fluids. This modification is motivated by unresolved issues regarding the global solvability of the classical system in situations where viscous hea...

Descripción completa

Detalles Bibliográficos
Autores: Díaz Díaz, Jesús Ildefonso, Rakotoson, J.M., Schmidt, P.G.
Tipo de recurso: artículo
Fecha de publicación:2008
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/51369
Acceso en línea:https://hdl.handle.net/20.500.14352/51369
Access Level:acceso abierto
Palabra clave:517.9
Boussinesq approximation
viscous heating
parabolic system
strong solutions.
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
Descripción
Sumario:We propose a modification of the classical Navier-Stokes-Boussinesq system of equations, which governs buoyancy-driven flows of viscous, incompressible fluids. This modification is motivated by unresolved issues regarding the global solvability of the classical system in situations where viscous heating cannot be neglected. A simple model problem leads to a coupled system of two parabolic equations with a source term involving the square of the gradient of one of the unknowns. In the present paper, we establish the local-in-time existence and uniqueness of strong solutions for the model problem. The full system of equations and the global-in-time existence of weak solutions will be addressed in forthcoming work.