Invariant manifolds and long-time asymptotics for the Vlasov--Poisson--Fokker--Planck equation (Q2753558)
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scientific article; zbMATH DE number 1670361
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Invariant manifolds and long-time asymptotics for the Vlasov--Poisson--Fokker--Planck equation |
scientific article; zbMATH DE number 1670361 |
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11 November 2001
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polynomially weighted Sobolev spaces
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similarity variable transformations
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asymptotics of small solutions
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Invariant manifolds and long-time asymptotics for the Vlasov--Poisson--Fokker--Planck equation (English)
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The author considers the Vlasov-Poisson-Fokker-Planck equation without a friction term in \(N\) dimensions. In a neighborhood of the origin in suitable polynomially weighted Sobolev spaces, finite-dimensional invariant manifolds are constructed by similarity variable transformations and spectral properties of the linearized problem. This construction implies detailed results about the long term asymptotics of small solutions.
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