Local and global solutions to Stokes-Magneto equations with fractional dissipations

Abstract

In this paper, we investigate a Stokes-Magneto system with fractional diffusions. We first deal with the non-resistive case in Td and establish the local and global well-posedness with initial magnetic field b0∈Hs(Td). We also show the existence of a unique mild solution of the resistive case with initial data b0 in the critical Lp(Rd) space. Moreover, we show that ‖b(t)‖Lp converges to zero as t→∞ when the initial data is sufficiently small. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.