The stochastic tamed MHD equations: existence, uniqueness and invariant measures

Abstract We study the tamed magnetohydrodynamics equations, introduced recently in a paper by author, perturbed multiplicative Wiener noise of transport type on whole space $${\mathbb {R}}^{3}$$ R 3 and torus {T}}^{3}$$ T . In first step, existence unique strong solution are established constructing weak solution, proving that pathwise uniqueness holds using Yamada–Watanabe theorem. then associated Markov semigroup prove it has Feller property. Finally, an invariant measure equation is shown for case torus.