The stochastic MHD equations driven by pure jump noise in Lp spaces

Abstract

We consider the stochastic incompressible magnetohydrodynamic equations driven by additive jump noises on either the whole space $R^d$, $d=2,3$ or a smooth bounded domain $D$ in $R^d$. We establish the local existence and uniqueness of a mild solution in the space $L^q(0,T;L_{\sigma }^{p\otimes }\left(D\right))$ allowing for initial data with less regularity, including the marginal case $u_0\in L_{\sigma }^{d\otimes }\left(D\right)$. In the two-dimensional case, we also prove the global existence of mild solutions.