Strong Feller property of the magnetohydrodynamics system forced by space–time white noise

The magnetohydrodynamics system forced by space–time white noise has been proposed and investigated by physicists and engineers, although without rigorous mathematical proofs of its solution's fundamental properties. Applying the theory of regularity structures, we prove its well-posedness and strong Feller property. The proof requires a careful treatment of nonlinear terms which are sensitive to specific components of the solution that is a six-dimensional vector field, of which the first three and the last three are velocity and magnetic fields, respectively. (paper)