Global Well-Posedness of 3d Axisymmetric MHD-Boussinesq System with Nonzero Swirl

In this paper, we consider the 3d axisymmetric MHD-Boussinesq system with nonzero swirl, and prove that the system, with initial data (u(0), h(0), rho(0)) = (u(0)(r)e(r) + u(0)(theta)e(theta) + u(0)(z)e(z), h(0)(theta)e(theta), rho(0)) which satisfies some small nonlinear condition, admits a global unique solution (u, h, rho) . Furthermore, some continuation criteria that imply regularity of axisymmetric solutions are also obtained.

Automated summary

In this paper, the 3d axisymmetric MHD-Boussinesq system with nonzero swirl is considered and it is proven that the system, with certain initial data satisfying small nonlinear conditions, has a global unique solution. Furthermore, some continuation criteria implying regularity of axisymmetric solutions are obtained.