%0 Journal Article
%A Díaz Díaz, Jesús Ildefonso
%A Rakotoson, J.M.
%A Schmidt, P.G.
%T Local strong solutions of a parabolic system related tothe Boussinesq approximation for buoyancy-driven flowwith viscous heating
%D 2008
%@ 1079-9389
%U https://hdl.handle.net/20.500.14352/51369
%X 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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