BKM-type blow-up criterion of the inviscid axially symmetric Boussinesq system involving a single component of velocity.

In this paper, we give a BKM-type blow-up criterion, which involves only a single component of the velocity, for the inviscid axially symmetric Boussinesq system. More precisely, we will show that if the vorticity of the swirl part of the velocity belongs to L 1 (0 , T ∗ , L ∞) , then the solution is regular up to time T ∗ . At present, our results can not be easily generalized to the classical L t 1 B M O regularity criterion, which will be considered in our further works. [ABSTRACT FROM AUTHOR]