Illner, Reinhard; Rein, Gerhard Time decay of the solutions of the Vlasov-Poisson system in the plasma physical case. (English) Zbl 0872.35087 Math. Methods Appl. Sci. 19, No. 17, 1409-1413 (1996). A new identity satisfied by solutions of the Vlasov-Poisson system is established and shown to have the property that all quantities involved have a definite sign. This property is then used to prove new results concerning the time decay of solutions governing certain physical systems. Reviewer: A.Jeffrey (Newcastle upon Tyne) Cited in 1 ReviewCited in 44 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 35B40 Asymptotic behavior of solutions to PDEs 82D10 Statistical mechanics of plasmas Keywords:time decay; Vlasov-Poisson system; plasma PDFBibTeX XMLCite \textit{R. Illner} and \textit{G. Rein}, Math. Methods Appl. Sci. 19, No. 17, 1409--1413 (1996; Zbl 0872.35087) Full Text: DOI References: [1] Batt, Arch. Rational Mech. Anal. 93 pp 159– (1986) [2] Glassey, Contemp. Math. 28 pp 269– (1984) · Zbl 0556.35122 · doi:10.1090/conm/028/751989 [3] Horst, Math. Meth. in the Appl. Sci. 4 pp 19– (1982) [4] Horst, Commun. Math. Phys. 126 pp 613– (1990) [5] Horst, Math. Meth. in the Appl. Sci. 16 pp 75– (1993) [6] Illner, Math. Meth. in the Appl. Sci. 17 pp 349– (1994) [7] Lions, Invent. math. 105 pp 415– (1991) [8] Pfaffelmoser, J. Diff. Eqns. 95 pp 281– (1992) [9] Schaeffer, Commun. Part. Diff. Eqns. 16 pp 1313– (1991) [10] ’Time decay, propagation of low moments and kinetic equations’, preprint 1995. [11] Rein, Math. Nachr. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.