The optimal decay estimates on the framework of Besov spaces for the Euler–Poisson two-fluid system

Abstract

In this paper, we are concerned with the optimal decay estimates for the Euler–Poisson two-fluid system. It is first revealed that the irrotationality of the coupled electronic field plays a key role such that the two-fluid system has the same dissipative structure as generally hyperbolic systems satisfying the Shizuta–Kawashima condition. This fact inspires us to obtain decay properties for linearized systems in the framework of Besov spaces. Furthermore, various decay estimates of solution and its derivatives of fractional order are deduced by time-weighted energy approaches in terms of low-frequency and high-frequency decompositions. As the direct consequence, the optimal decay rates of Lp(ℝ3)-L2 (ℝ3) (1 ≤ p < 2) type for the Euler–Poisson two-fluid system are also shown. Compared with previous works in Sobolev spaces, a new observation is that the difference of variables exactly consists of a one-fluid Euler–Poisson equations, which leads to the sharp decay estimates for velocities.