Article

# On the global well-posedness for Boussinesq system

Université de Rennes, 1, Campus de Beaulieu, 35042 Rennes cedex, France
Journal of Differential Equations 01/2007; DOI:10.1016/j.jde.2006.10.008

ABSTRACT In this paper, we give a global well-posedness result for the two-dimensional Boussinesq system with partial viscosity, when the initial data and .

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ABSTRACT: We prove the global well-posedness of the viscous incompressible Boussi-nesq equations in two spatial dimensions for general initial data in H m with m ≥ 3. It is known that when both the velocity and the density equations have finite posi-tive viscosity, the Boussinesq system does not develop finite time singularities. We consider here the challenging case when viscosity enters only in the velocity equation, but there is no viscosity in the density equation. Using sharp and delicate energy estimates, we prove global existence and strong regularity of this viscous Boussinesq system for general initial data in H m with m ≥ 3.
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