Osgood type blow-up criterion for the 3D Boussinesq equations with partial viscosity

AIMS Mathematics

Zhaoyang Shang¹ 

[1] School of Mathematical Science, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;

关键词: Boussinesq equations| blow-up criterion| Besov space;   

DOI  :  10.3934/Math.2018.1.1

来源: DOAJ

【 摘 要 】

This paper is dedicated to studying the blow-up criterion of smooth solutions to the three-dimensional Boussinesq equations with partial viscosity. By means of the Littlewood-Paley decomposition, we give an improved logarithmic Sobolev inequality and through this, we obtain the correspondingblow-up criterion in a space larger than $\dot{B}^0_{\infty,\infty}$, which extends several previous works.

【 授权许可】

Unknown