STABILITY OF THE PLANAR RAREFACTION WAVE TO THREE-DIMENSIONAL COMPRESSIBLE MODEL OF VISCOUS IONS MOTION

The compressible Navier-Stokes-Poisson equations model the motion of viscous ions and play important roles in the study of self-gravitational viscous gaseous stars and in the simulations of charged particles in semiconductor devices and plasmas physics. This paper establishes the stability and precise large-time behavior of perturbations near the planar rarefaction wave to three-dimensional isentropic compressible Navier-Stokes-Poisson equations. The results presented in this paper are new. Previous studies focused on the one-dimensional compressible Navier-Stokes-Poisson equations and little has been done for the multi-dimensional case. In order to prove the desired asymptotic stability, we take into account both the effect of the self-consistent electrostatic potential and the decay rate of the planar rarefaction wave. Due to the complexity of the nonlinearity and the effect of the self-consistent electric field, the proof involves highly non-trivial a priori bounds.