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arXiv · 0910.0311

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

Changxing Miao·Liutang Xue
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Abstract

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

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Changxing Miao, Liutang Xue. 2009-10-02. On the global well-posedness of a class of Boussinesq- Navier-Stokes systems. https://doi.org/10.1007/s00030-011-0114-5

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