Geodesic
A note on global regularity results for 2D Boussinesq equations with fractional dissipation
Zhuan Ye1
1 Department of Mathematics and Statistics Jiangsu Normal University 101 Shanghai Road Xuzhou 221116, Jiangsu, P.R. China
Annales Polonici Mathematici, Tome 117 (2016) no. 3, pp. 231-247.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We study the Cauchy problem for the two-dimensional (2D) incompressible Boussinesq equations with fractional Laplacian dissipation and thermal diffusion. Invoking the energy method and several commutator estimates, we get a global regularity result for the 2D Boussinesq equations as long as $1-\alpha \lt \beta \lt \min\left\{\frac{\alpha}{2}, \frac{3\alpha-2}{2\alpha^{2}-6\alpha+5}, \frac{2-2\alpha}{4\alpha-3}\right\}$ with $0.77963\thickapprox\alpha_{0} \lt \alpha \lt 1$. This improves on some previous work.
DOI : 10.4064/ap3784-10-2015
Keywords: study cauchy problem two dimensional incompressible boussinesq equations fractional laplacian dissipation thermal diffusion invoking energy method several commutator estimates get global regularity result boussinesq equations long alpha beta min frac alpha frac alpha alpha alpha frac alpha alpha right thickapprox alpha alpha improves previous work

Zhuan Ye 1

1 Department of Mathematics and Statistics Jiangsu Normal University 101 Shanghai Road Xuzhou 221116, Jiangsu, P.R. China 
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Zhuan Ye. A note on global regularity results for 2D Boussinesq equations with fractional dissipation. Annales Polonici Mathematici, Tome 117 (2016) no. 3, pp. 231-247. doi : 10.4064/ap3784-10-2015. http://geodesic.mathdoc.fr/articles/10.4064/ap3784-10-2015/

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