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...
| Autores: | , , |
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| 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 |
| 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. |
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