On the global well-posedness of a class of Boussinesq- Navier-Stokes systems

Details On the global well-posedness of a class of Boussinesq- Navier-Stokes systems On the global well-posedness of a class of Boussinesq- Navier-Stokes systems

2009-10-02

arxiv.org/abs/0910.0311v1

Nonlinear Differ. Equ. Appl. 18 (2011), 707-735

Mathematics

Analysis of PDEs

23pages

Scientific paper

10.1007/s00030-011-0114-5

In this paper we consider the following 2D Boussinesq-Navier-Stokes systems \partial_{t}u+u\cdot\nabla u+\nabla p+ |D|^{\alpha}u &= \theta e_{2} \partial_{t}\theta+u\cdot\nabla \theta+ |D|^{\beta}\theta &=0 \quad with $\textrm{div} u=0$ and $0<\beta<\alpha<1$. When $\frac{6-\sqrt{6}}{4}<\alpha< 1$, $1-\alpha<\beta\leq f(\alpha) $, where $f(\alpha)$ is an explicit function as a technical bound, we prove global well-posedness results for rough initial data.

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