#### Vol. 298, No. 1, 2019

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Global well-posedness for the 2D fractional Boussinesq Equations in the subcritical case

### Daoguo Zhou, Zilai Li, Haifeng Shang, Jiahong Wu, Baoquan Yuan and Jiefeng Zhao

Vol. 298 (2019), No. 1, 233–255
DOI: 10.2140/pjm.2019.298.233
##### Abstract

We study the global regularity of solutions to the 2D Boussinesq equations with fractional dissipation, given by ${\left(-\Delta \right)}^{\alpha ∕2}u$ in the velocity equation and by ${\left(-\Delta \right)}^{\beta ∕2}\theta$ in the temperature equation. We establish the global regularity for $\frac{2}{3}<\alpha <1$, $\alpha +\beta >1$ and $\alpha >\frac{1}{1+\beta }$. This result is for the subcritical regime $\alpha +\beta >1$ and the point here is to obtain the global regularity for the largest possible range of $\alpha$.

##### Keywords
Boussinesq equations, fractional dissipation, global regularity
##### Mathematical Subject Classification 2010
Primary: 35B65, 35Q35
Secondary: 76B03, 76A10