The stochastic MHD equations driven by pure jump noise in $L^p$ spaces

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

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