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-infinity), then the solution is regular up to time T-*. At present, our results can not be easily generalized to the classical L-t(1) BMO regularity criterion, which will be considered in our further works.