Stability of non-constant equilibrium solutions for two-fluid Euler–Maxwell systems

In this work we consider periodic problems for two-fluid compressible Euler–Maxwell systems for plasmas. The initial data are supposed to be in a neighborhood of non-constant equilibrium states. Mainly by an induction argument used in Peng (2015), we prove the global stability in the sense that smooth solutions exist globally in time and converge to the equilibrium states as the time goes to infinity. Moreover, we obtain the global stability of solutions with exponential decay in time near the equilibrium states for two-fluid compressible Euler–Poisson systems.