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On the Cauchy Problem of the Vlasov-Poisson-BGK System: Global Existence of Weak Solutions

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Abstract

Global-in-time existence of weak solutions to the Cauchy problem of the three dimensional Vlasov-Poisson-BGK system is shown for initial data belonging to the space L p(ℝ3×ℝ3) with p>9 and having finite second order velocity moments. This result solves partially the well-posed problem for the Vlasov-Poisson-BGK system proposed by B. Perthame: “Higher moments for kinetic equations: the Vlasov-Poisson and Fokker-Planck cases,” Math. Meth. Appl. Sci. 13:441–452, 1990.

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  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, People’s Republic of China

    Xianwen Zhang

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Zhang, X. On the Cauchy Problem of the Vlasov-Poisson-BGK System: Global Existence of Weak Solutions. J Stat Phys 141, 566–588 (2010). https://doi.org/10.1007/s10955-010-0064-z

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  • DOI: https://doi.org/10.1007/s10955-010-0064-z

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