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Local strong solutions of a parabolic system related to the Boussinesq approximation for buoyancy-driven flow with viscous heating

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Díaz Díaz, Jesús Ildefonso and Rakotoson, J.M. and Schmidt, P.G. (2008) Local strong solutions of a parabolic system related to the Boussinesq approximation for buoyancy-driven flow with viscous heating. Advances in Differential Equations, 13 (9-10). pp. 977-1000. ISSN 1079-9389

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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Boussinesq approximation; viscous heating; parabolic system,;strong solutions.
Subjects:Sciences > Mathematics > Differential equations
ID Code:30197
Deposited On:21 May 2015 07:41
Last Modified:12 Dec 2018 15:07

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