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October  2000, 6(4): 751-772. doi: 10.3934/dcds.2000.6.751

Regular solutions of the Vlasov-Poisson-Fokker-Planck system

Kosuke Ono 1, and  Walter A. Strauss 2,

1. 

Department of Mathematical and Natural Sciences, The University of Tokushima, 1-1 Minamijosanjima-cho, Tokushima 770-8502
2. 

Department of Mathematics and LCDS, Brown University, Providence, RI 02912, United States

Received  May 2000 Revised  July 2000 Published  August 2000

We study the Vlasov-Poisson-Fokker-Planck system. For arbitrary data we prove the global well-posedness and gain of regularity of solutions under improved assumptions. We also prove that if the initial data are sufficiently small, the solutions satisfy optimal rates of asymptotic decay.
Keywords: Fokker-Planck equation, regularity, asymptotic behavior., Kinetic theory, Vlasov-Poisson-Fokker-Planck system, plasma physics.
Mathematics Subject Classification: Primary: 82D10, 76X05, 35B60, 35B4.
Citation: Kosuke Ono, Walter A. Strauss. Regular solutions of the Vlasov-Poisson-Fokker-Planck system. Discrete & Continuous Dynamical Systems, 2000, 6 (4) : 751-772. doi: 10.3934/dcds.2000.6.751
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