Global Existence Results for the Anisotropic Boussinesq System in Dimension Two
Analysis of PDEs
2013-02-27 v1
Abstract
We study the global existence issue for the two-dimensional Boussinesq system with horizontal viscosity in only one equation. We first examine the case where the Navier-Stokes equation with no vertical viscosity is coupled with a transport equation. Second, we consider a coupling between the classical two-dimensional incompressible Euler equation and a transportdiffusion equation with diffusion in the horizontal direction only. For the both systems and for arbitrarily large data, we construct global weak solutions `a la Leray. Next, we state global wellposedness results for more regular data. Our results strongly rely on the fact that the diffusion occurs in a direction perpendicular to the buoyancy force.
Keywords
Cite
@article{arxiv.0809.4984,
title = {Global Existence Results for the Anisotropic Boussinesq System in Dimension Two},
author = {Raphaël Danchin and Marius Paicu},
journal= {arXiv preprint arXiv:0809.4984},
year = {2013}
}