Global solutions of 3D axisymmetric Boussinesq equations with nonzero swirl

Considering the 3D axisymmetric Boussinesq system with nonzero swirl, we obtain the global existence and uniqueness of the strong solutions (u, rho), when parallel to r(d)u(0)(theta) parallel to(L) (3/1-d) d is an element of [0, 1], is sufficiently small. Furthermore, if u(0) is an element of L-3/2 (R-3) and ru(0)(theta) is an element of L-1(R-3) boolean AND L-2(R-3), we have the decay estimate parallel to u(t)parallel to(L2(R3)) + < t >(2) rho parallel to(t)parallel to(2)(L2(R3)) + < t >(2) parallel to u(theta)(t)parallel to(2)(L2(R3)) <= C < t >(-1/2), for any t > 0. At last, we get several continuation criteria. (C) 2017 Elsevier Ltd. All rights reserved.