Stability of the rarefaction wave for a two-fluid plasma model with diffusion

Abstract

We study the large-time asymptotics of solutions toward the weak rarefaction wave of the quasineutral Euler system for a two-fluid plasma model in the presence of diffusions of velocity and temperature under small perturbations of initial data and also under an extra assumption \begin{equation*} \frac{\theta_{i,+}}{\theta_{e,+}}=\frac{\theta_{i,-}}{\theta_{e,-}}\geq \frac{m_i}{2m_e}, \end{equation*} namely, the ratio of the thermal speeds of ions and electrons at both far fields is not less than one half. Meanwhile, we obtain the global existence of solutions based on energy method.