Local strong solutions of a parabolic system related to the Boussinesq approximation for buoyancy-driven ow with viscous heating
نویسندگان
چکیده
We propose a modi cation of the classical Navier-Stokes-Boussinesq system of equations, which governs buoyancy-driven ows of viscous, incompressible uids. This modi cation 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. Keywords. Boussinesq approximation, viscous heating, parabolic system, strong solutions. AMS subject classi cation. 35Q35, 35Q72, 35K45, 35K50.
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