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

Kosuke Ono; Walter A. Strauss

doi:10.3934/dcds.2000.6.751

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2000, Volume 6, Issue 4: 751-772. Doi: 10.3934/dcds.2000.6.751

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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

Received: April 30, 2000

Revised: June 30, 2000

Published: September 2000

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Abstract

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.

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Mathematics Subject Classification: Primary: 82D10, 76X05, 35B60, 35B40.

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