Existence and uniqueness of a global smooth solution for the Vlasov- Poisson-Fokker-Planck system in three dimensions
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.
scientific article; zbMATH DE number 220693