Díaz Díaz, Jesús Ildefonso and Rakotoson, Jean Michel Theresien and Schmidt, Paul G.
(2007)
*A parabolic system involving a quadratic gradient term related to the Boussinesq approximation.*
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A: Matemáticas , 101
(1).
pp. 113-118.
ISSN 1578-7303

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## Abstract

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.

Item Type: | Article |
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Uncontrolled Keywords: | equations; fluid |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 15290 |

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Deposited On: | 21 May 2012 09:53 |

Last Modified: | 06 Feb 2014 10:20 |

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