Abstract
The three-dimensional incompressible magnetohydrodynamic equations with stochastic external forces are considered. First the existence and uniqueness of local strong solution to the stochastic magnetohydrodynamic equations are proved when the external forces satisfy some conditions. The proof is based on the contraction mapping principle, stopping time and stochastic estimates. The strong solution is a weak solution for the fluid variables with a given complete probability space and a given Brownian motion. Then, the global existence of strong solutions in probability is established if the initial data are sufficiently small, and the noise is multiplicative and non-degenerate.
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