Existence and uniqueness of a global smooth solution for the Vlasov- Poisson-Fokker-Planck system in three dimensions
type: Item
instance of: scholarly article
title: Existence and uniqueness of a global smooth solution for the Vlasov- Poisson-Fokker-Planck system in three dimensions
zbMATH Open document ID: 0777.35059
author: François Bouchut
published in: Journal of Functional Analysis
publication date: 1993-06-29T00:00:00Z
review text: One proves the existence and the uniqueness of a smooth solution to the Vlasov-Poisson-Fokker-Planck equation in three dimensions. The problem is re-written by using Green's functions, whereby one can get various inequalities and estimates which allow the author to investigate the regularity of the density and of the induced field (field induced by the V-P-F-P equation). These results are the preliminary lemma which provide the proof of the main results. Then it is shown that there is uniqueness even for weak initial data.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 220693
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: smooth solution
zbMATH Keywords: Vlasov-Poisson-Fokker-Planck equation
zbMATH Keywords: Green's functions
zbMATH Keywords: density
zbMATH Keywords: induced field
zbMATH Keywords: weak initial data
Wikidata QID: Q57964854
reviewed by: Guy Jumarie
MaRDI profile type: Publication
full work available at URL: jfan.1993.1011
OpenAlex ID: W2032502639
DOI: 10.1006/JFAN.1993.1011
description: scientific article; zbMATH DE number 220693