Approximating three-dimensional magnetohydrodynamics system forced by space-time white noise

The magnetohydrodynamics system forced by space-time white noise has been studied by physicists for decades, and the rigorous proof of its solution theory was recently established by Yamazaki (2023, Electron. J. Probab., 28 , 1-66). When an equation is well-posed, and it is approximated by replacing the differentiation operator by reasonable discretization schemes, it is widely believed that a solution of the approximating equation should converge to the solution of the original equation as the discretization parameter approaches zero. We prove otherwise for the three-dimensional magnetohydrodynamics system forced by space-time white noise. Specifically, we prove that the limit of the solution to the approximating system with an additional 32 drift terms solves the original system. These 32 drift terms depend on the choice of approximations, can be calculated explicitly and essentially represent a spatial version of It & ocirc;-Stratonovich correction terms. (c) 2024 Elsevier Inc. All rights reserved.