Asymptotic stability of boundary layers to the Euler-Poisson equations arising in plasma physics (Q2904725)

A global existence theorem for the Euler-Poisson equation in weighted functional spaces is proven under the Bohm criterion. Consequently, the asymptotic stability of the stationary solution (so-called boundary layer) is stated. The proof of existence of the global-in-time solution is quite traditional: first, the local in time existence theorem is proven; next, the global existence theorem is proven with the use of a priori estimations previously deduced in the paper. It is worthy to notice a virtuous technic which the authors demonstrate while deducing the a priori estimations.