A regularity criterion for the 3D axisymmetric Boussinesq equations with non-zero swirl

In this paper, we are devoted to establishing a new regularity criterion of weak solutions to incompressible axisymmetric Boussinesq equations. More precisely, we prove that for a small epsilon > 0, if the angular component of velocity field u(theta)(t, r, z) satisfies sup0< t<T vertical bar vertical bar zu(theta vertical bar)vertical bar L-infinity||(Omega(delta)) <= epsilon, where Omega(delta) := {(x(1), x(2), z) epsilon R-3|root x(1)(2) + x(2)(2) < delta} denotes a thin cylinder with infinite height and radius delta > 0, which is independent of the initial data, then the weak solution (u,rho) to 3D Boussinesq equations is regular in (0, T].