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On time decay for the spherically symmetric Vlasov-Poisson system

In memory of Robert Glassey

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  • A collisionless plasma is modeled by the Vlasov-Poisson system. Solutions in three space dimensions that have smooth, compactly supported initial data with spherical symmetry are considered. An improved field estimate is presented that is based on decay estimates obtained by Illner and Rein. Then some estimates are presented that ensure only particles with sufficiently small velocity can be found within a certain (time dependent) ball.

    Mathematics Subject Classification: 35L60, 35Q83, 82C22, 82D10.

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  • [1] C. Bardos and P. Degond, Global existence for the Vlasov-Poisson equation in $3$ space variables with small initial data, Ann. Inst. H. Poincaré Anal. Non Linéaire, 2 (1985), 101-118.  doi: 10.1016/S0294-1449(16)30405-X.
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    [8] R. GlasseyS. Pankavich and J. Schaeffer, On long-time behavior of monocharged and neutral plasma in one and one-half dimensions, Kinet. Relat. Models, 2 (2009), 465-488.  doi: 10.3934/krm.2009.2.465.
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    [12] P.-L. Lions and B. Perthame, Propagation of moments and regularity for the $3$-dimensional Vlasov-Poisson system, Invent. Math., 105 (1991), 415-430.  doi: 10.1007/BF01232273.
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    [17] J. Schaeffer, Large-time behavior of a one-dimensional monocharged plasma, Differential Integral Equations, 20 (2007), 277-292. 
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