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2008 Local strong solutions of a parabolic system related to the Boussinesq approximation for buoyancy-driven flow with viscous heating
J. I. Díaz, J. M. Rakotoson, P. G. Schmidt
Adv. Differential Equations 13(9-10): 977-1000 (2008).

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.

Citation

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J. I. Díaz. J. M. Rakotoson. P. G. Schmidt. "Local strong solutions of a parabolic system related to the Boussinesq approximation for buoyancy-driven flow with viscous heating." Adv. Differential Equations 13 (9-10) 977 - 1000, 2008.

Information

Published: 2008
First available in Project Euclid: 18 December 2012

zbMATH: 1230.35097
MathSciNet: MR2482584

Subjects:
Primary: 35K55
Secondary: 35Q35, 76D03, 76D05

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.13 • No. 9-10 • 2008
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