Well-posedness and large-time behavior for the two-phase system with magnetic field in critical Besov spaces

This paper is dedicated to the study of the two-phase system with magnetic field in multi-dimensional spaces d >= 2$d\ge 2$. We investigate the local and global well-posedness of strong solutions to the Cauchy problem in critical Besov spaces. Moreover, a Lyapunov-type energy argument can be developed, which leads to the time-decay estimates of solutions without additional smallness assumptions. We improve the previous effects obtained by Wen and Zhu (JDE-2018), Wang and Cheng (AMS-2022), where they established the global well-posedness of strong solutions in the H2(R3)$ H<^>{2}(\mathbb {R}<^>{3})$-norm Sobolev spaces.