The global convergence of non-isentropic Euler–Maxwell equations via Infinity-Ion-Mass limit

Abstract

This paper is concerned with the periodic problem to the two-fluid non-isentropic Euler–Maxwell (N-E-M) equations. The equations arises in the modeling of magnetic plasma, in which appear two physical parameters, the mass of an electron $$m_\mathrm{e}$$ and the mass of an ion $$m_{\mathrm{i}}$$ . With the help of methods of asymptotic expansions, we prove the local-in-time convergence of smooth solutions to this problem by setting $$m_\mathrm{e} = 1$$ and letting $$m_{\mathrm{i}} \rightarrow +\infty $$ . Moreover, when the initial data are near constant equilibrium states, by means of uniform energy estimates and compactness arguments, we rigorously prove the infinity-ion-mass convergence of the system for all time. The limit system is the one-fluid N-E-M system.