Global Axisymmetric Solutions of Three Dimensional Inhomogeneous Incompressible Navier-Stokes System with Nonzero Swirl

In this paper, we investigate the global well-posedness for the three dimensional inhomogeneous incompressible Navier-Stokes system with axisymmetric initial data. We obtain the global existence and uniqueness of the axisymmetric solution provided that parallel to a(0)/r parallel to(infinity) and parallel to u(0)(theta)parallel to(3) are sufficiently small. Furthermore, if u(0) is an element of L-1 and ru(0)(theta) is an element of L-1 boolean AND L-2, we have the decay estimate parallel to u(theta)(t)parallel to(2)(2) + < t > parallel to del(u(theta)e(theta))(t)parallel to(2)(2) + t < t >(parallel to u(t)(theta)(t)parallel to(2)(2) + parallel to Delta(u(theta)e(theta))(t)parallel to(2)(2)) <= C < t >(-5/2), (sic) t > 0.