Global weak solution of the vlasov–poisson system for small electrons mass

We are studying the existence and weak stability of a Vlasov–Poisson syste with two typs of particles , in which the electrons are supposed to be at thermal equilibrium. This modifies the source term in the Poisson equaitonm\, and estimates in the Marcinkiewicz space M3 for the potential are used to get the strong compactness of approximations using a new regularized kernal which preservs an approriate energy inequality.