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

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Díaz Díaz, Jesús Ildefonso and Rakotoson, Jean Michel Theresien and 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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Abstract

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.


Item Type:Article
Uncontrolled Keywords:equations; fluid
Subjects:Sciences > Mathematics > Differential equations
ID Code:15290
Deposited On:21 May 2012 09:53
Last Modified:12 Dec 2018 15:07

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