论文标题
随机驯服的MHD方程 - 存在，唯一性和不变措施
The Stochastic Tamed MHD Equations -- Existence, Uniqueness and Invariant Measures
论文作者
论文摘要
我们研究了作者最近在一篇论文中引入的驯服磁性水力动力学方程，并在整个空间上的乘法运输噪声$ \ mathbb {r}^{3} $以及在torus $ \ mathbb {t}^{3} $上扰动。第一步，通过构建弱解决方案来确定独特的强解决方案的存在，证明路径界唯一性保持并使用Yamada-Watanabe定理。然后，我们研究了相关的Markov Semigroup，并证明它具有坠机财产。最后，为圆环的情况显示了方程式的不变度度量的存在。
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.
