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Existence and uniqueness of a global smooth solution for the Vlasov- Poisson-Fokker-Planck system in three dimensions. (English) Zbl 0777.35059
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.

MSC:
35Q35 PDEs in connection with fluid mechanics
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B65 Smoothness and regularity of solutions to PDEs
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