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

中文翻译：

---

随机驯服的 MHD 方程：存在性、唯一性和不变测度

我们研究了作者最近在一篇论文中介绍的驯服的磁流体动力学方程，受到整个空间\({\mathbb {R}}^{3}\)和环面\({ \mathbb {T}}^{3}\)。第一步，通过构造弱解，证明路径唯一性成立并使用 Yamada-Watanabe 定理，建立唯一强解的存在性。然后我们研究相关的马尔可夫半群并证明它具有费勒性质。最后，对于环面的情况显示了方程的不变测度的存在。