American Institute of Mathematical Sciences

September  2015, 8(3): 395-411. doi: 10.3934/krm.2015.8.395

On the well-posedness of the inviscid Boussinesq equations in the Besov-Morrey spaces

 1 School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China, China 2 Department of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, China

Received  March 2014 Revised  December 2014 Published  June 2015

This paper is devoted to the study of the inviscid Boussinesq equations. We establish the local well-posedness and blow-up criteria in Besov-Morrey spaces $N_{p,q,r}^s(\mathbb{R}^n)$ for super critical case $s > 1 + \frac{n}{p}, 1 < q \leq p < \infty, 1 \leq r\leq \infty$, and critical case $s=1+\frac{n}{p}, 1 < q \leq p < \infty, r=1$. Main analysis tools are Littlewood-Paley decomposition and the paradifferential calculus.
Citation: Qunyi Bie, Qiru Wang, Zheng-An Yao. On the well-posedness of the inviscid Boussinesq equations in the Besov-Morrey spaces. Kinetic & Related Models, 2015, 8 (3) : 395-411. doi: 10.3934/krm.2015.8.395
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