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

By Changxing Miao, Liutang Xue. 2009

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AbstractIn this paper we consider the following 2D Boussinesq–Navier–Stokes systems $${\begin{array}{lll}\partial_t u + u \cdot \nabla u + \nabla p = - \nu |D|^\alpha u + \theta e_2\\ \quad\quad \partial_t \theta+u\cdot\nabla \theta = - \kappa|D|^\beta \theta \\ \quad\quad\quad\quad\quad{\rm div} u = 0\end{array}}$$with ν > 0, κ > 0 and 0 < β < α < 1. When $${\frac{6-\sqrt{6}}{4}({\doteq}0.888) < \alpha < 1, 1-\alpha < \beta \leq f(\alpha)}$$, where f(α) < 1 is an explicit function as a technical bound, we prove the global well-posedness results for the rough initial data.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d29d47991db9731c0814e39316fc02046afba816