On the statistical solutions of Vlasov-Poisson equations in two dimensions
The problem studied in the paper is that of Vlasov bidimensional flow with a singular Poisson kernel. It is treated with statistical methods, used already by \textit{A. A. Arsen'ev} in Dokl. Akad. Nauk SSSR 220, 1249- 1250 (1975; Zbl 0342.35050). The presence of the singular Poisson kernel makes the convergence proof very difficult, so that the authors elaborated a new convergence method, based on a Galerkin approximation procedure, for which the convergence was proved by the authors in Z. Angew. Math. Phys. 35, 790-801 (1984; Zbl 0547.65082). The uniqueness of the solution is also proved.
scientific article; zbMATH DE number 3976644
scientific article