Global smooth solution for a kind of two-fluid system in plasmas

A kind of two-fluid system in plasmas is studied in this paper. This system describes rich dynamics of a plasma, including the interactions between the ion acoustic wave and the plasma wave. When ignoring the effect of the high-frequency electric field, such system reduces to the ion type Euler–Poisson system. We prove that for this kind of two-fluid system, small perturbations around the equilibrium state lead to a global smooth solution. This result generalizes the recent work given by Guo and Pausader.