On the statistical solutions of Vlasov-Poisson equations in two dimensions
type: Item
instance of: scholarly article
title: On the statistical solutions of Vlasov-Poisson equations in two dimensions
zbMATH Open document ID: 0604.76064
DOI: 10.1007/BF00945293
author: B. George
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 82B05
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 3976644
zbMATH Keywords: Vlasov bidimensional flow
zbMATH Keywords: singular Poisson kernel
zbMATH Keywords: statistical methods
zbMATH Keywords: convergence
zbMATH Keywords: Galerkin approximation procedure
zbMATH Keywords: uniqueness
reviewed by: Ştefan Zanfir
MaRDI profile type: Publication
cites work: Statistical study of Navier-Stokes equations. I
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description: scientific article; zbMATH DE number 3976644