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

The magnetohydrodynamics system consists of the Navier-Stokes and Maxwell's equations, coupled through multiples nonlinear terms. Such a forced by space-time white noise has been studied physicists for decades, rigorous proof its solution theory recently established in Yamazaki (2019, arXiv:1910.04820 [math.AP]) using paracontrolled distributions technique renormalizations. When an equation is well-posed, it approximated replacing differentiation operator reasonable discretization schemes with parameter, widely believed that approximating should converge to original as parameter approaches zero. We prove otherwise case three-dimensional noise. Specifically, proven limit additional 32 drift terms solves system. These depend on choice approximations, can be calculated explicitly process renormalizations, essentially represent spatial version It$\hat{\mathrm{o}}$-Stratonovich correction In particular, relies renormalizations again, well taking advantage special structure many occasions.