Modeling and analysis of stochastic quantum magnetohydrodynamics equations with energy estimates

This manuscript investigates the three-dimensional stochastic compressible quantum magnetohydrodynamic equation with density-dependent and stochastic external forces. First, we approximate the modelled system. In this work, the existence of a martingale solution within a given time interval is established by deriving energy estimates and applying the fixed-point argument. The proposed system is approximated using the Faedo-Galerkin method, the Jakubowski-Skorokhod theorem, and the compactness method. Furthermore, the result is analyzed in the limit n → ∞ and η → 0. Finally, numerical results for the quantum magnetohydrodynamic system are presented for the demonstrated theoretical findings.