%0 Journal Article
%A Díaz Díaz, Jesús Ildefonso
%A Rakotoson, Jean Michel Theresien
%A Schmidt, Paul G.
%T A parabolic system involving a quadratic gradient term related to the Boussinesq approximation
%D 2007
%@ 1578-7303
%U https://hdl.handle.net/20.500.14352/49944
%X 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.
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