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Global classical solutions of the periodic Vlasov-Poisson system in three dimensions. (English. Abridged French version) Zbl 0741.35058
(Authors’ summary.) In connection with recent results on the global existence of classical solutions of the Vlasov-Poisson system on \(\mathbb{R}^ 3\times \mathbb{R}^ 3\) obtained by K. Pfaffelmoser [e.g.: Globale klassische Lösungen des dreidimensionalen Vlasov-Poisson- Systems. Diss. Univ. München, Fak. Math. (1989; Zbl 0722.35090)], J. Schaeffer [e.g.: Commun. Partial Differ. Equations 16, No. 8/9, 1313- 1335 (1991); J. Differ. Equations 69, 111-148 (1987; Zbl 0642.35058)], and E. Horst [e.g.: Math. Methods Appl. Sci. 3, 229-248 (1981; Zbl 0463.35071); Diss. Math. 292, 63 p. (1990; Zbl 0725.35105)] we prove the existence of global classical solutions of the corresponding system for a neutral plasma on \(Q\times \mathbb{R}^ 3\), where \(Q\) is the unit cube in \(\mathbb{R}^ 3\) and Poisson’s equation is solved on \(Q\) with periodic boundary conditions. This result is relevant in connection with the authors’ recent investigation of the stability of stationary solutions of the Vlasov-Poisson system [J. Batt, e.g.: Appl. Math. Technol., Proc. Ger.-Ital. Symp., Rome 1984, 375-385 (1984; Zbl 0599.76147); G. Rein, e.g.: Commun. Math. Phys. 135, No. 1, 41-78 (1990; Zbl 0722.35091)].
Reviewer: M.Biroli (Monza)

35Q35 PDEs in connection with fluid mechanics