Stability of non-constant equilibrium solutions for two-fluid non-isentropic Euler-Maxwell systems arising in plasmas

Abstract

We consider the periodic problem for two-fluid non-isentropic Euler-Maxwell systems in plasmas. By means of suitable choices of symmetrizers and an induction argument on the order of the time-space derivatives of solutions in energy estimates, the global smooth solution with small amplitude is established near a non-constant equilibrium solution with asymptotic stability properties. This improves the results obtained in the work of Li et al. [Z. Angew. Math. Phys. 67(5), 133 (2016)] for models with temperature diffusion terms by using the pressure functions pν in place of the unknown variable densities nν.