GLOBAL CONVERGENCE IN INFINITY-ION-MASS LIMITS FOR BIPOLAR EULER-POISSON SYSTEM

This paper concerns the global-in-time convergence from bipolar Euler-Poisson system (BEP) to unipolar Euler-Poisson system (UEP) through the infinity-ion-mass limit by letting the ratio of the mass of ions over that of electrons go to infinity. Applying the stream function method and making full use of the anti-symmetric structure of the error system, we carry out global-in-time convergence analysis of this limit and establish global-in-time error estimates between smooth solutions to BEP and UEP. It is worth mentioning that due to the strong coupling through the Poisson equation in bipolar system, stream functions for ion and electron equations should be constructed respectively based on asymptotic expansions of solutions, which is very different from the case for unipolar systems.