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

2024/12/17 by Kun Ni, Ni, Kaicheng, Heling Su +3
Economics, Econometrics and Finance · Mathematics · Engineering · #Stochastic processes and financial applications #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2412.12577

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;\mathbbL^p⊗_σ(D)) allowing for initial data with less regularity, including the marginal case u₀∈ \mathbbL^d⊗_σ(D). In the two-dimensional case, we also prove the global existence of mild solutions.

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