The global well-posedness of solutions to compressible isentropic two-fluid magnetohydrodynamics in a strip domain

In this paper, we consider a model of compressible isentropic two-fluid magneto-hydrodynamics without resistivity in a strip domain in three dimensional space. By exploiting the two-tier energy method developed in [Anal PDE, 2013, 6: 1429–1533], we prove the global well-posedness of the governing model around a uniform magnetic field which is non-parallel to the horizontal boundary. Moreover, we show that the solution converges to the steady state at an almost exponential rate as time goes to infinity. Compared to the work of Tan and Wang [SIAM J Math Anal, 2018, 50: 1432–1470], we need to overcome the difficulties caused by particles.