LONG WAVELENGTH LIMIT OF NON-ISENTROPIC EULER-POISSON SYSTEM

This paper is devoted to study the long wavelength limit of EulerPoisson system with variable temperature for ions in plasma. By the GardnerMorikawa transformation, we formally derive the Korteweg-de Vries (KdV) equation and the linear KdV equation from the non-isentropic Euler-Poisson system. Then, we establish the rigorous justification of the KdV equation from Euler-Poisson equation in a time interval [0, tau*epsilon- 32 ] for some tau* > 0. The long wavelength limit of Euler-Poisson equation follows from the suitable uniform bound of the remainder terms by the nonlinear energy estimates.