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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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.
|Uncontrolled Keywords:||equations; fluid|
|Subjects:||Sciences > Mathematics > Differential equations|
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|Deposited On:||21 May 2012 11:53|
|Last Modified:||16 May 2013 20:02|
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