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A parabolic system involving a quadratic gradient term related to the Boussinesq approximation


Díaz Díaz, Jesús Ildefonso y Rakotoson, Jean Michel Theresien y Schmidt, Paul G. (2007) A parabolic system involving a quadratic gradient term related to the Boussinesq approximation. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A: Matemáticas , 101 (1). pp. 113-118. ISSN 1578-7303

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We propose a modification of the classical Boussinesq approximation for buoyancy-driven flows of viscous, incompressible fluids in situations where viscous heating cannot be neglected. This modification is motivated by unresolved issues regarding the global solvability of the original system. A very 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. Based on adequate notions of weak and strong solutions, we establish the global-in-time existence of weak solutions and the uniqueness of strong solutions.

Tipo de documento:Artículo
Palabras clave:equations; fluid
Materias:Ciencias > Matemáticas > Ecuaciones diferenciales
Código ID:15290

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Depositado:21 May 2012 09:53
Última Modificación:06 Feb 2014 10:20

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