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  Optimal gradient estimates and asymptotic behaviour for the Vlasov-Poisson system with small initial data

Hwang, H. J., Rendall, A. D., & Velazquez, J. J. L. (2011). Optimal gradient estimates and asymptotic behaviour for the Vlasov-Poisson system with small initial data. Archive for Rational Mechanics and Analysis, 200 (1), 313-360. doi:10.1007/s00205-011-0405-3.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5F9F-5 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5FA1-E
Genre: Journal Article

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 Creators:
Hwang, Hyung Ju, Author
Rendall, Alan D.1, Author              
Velazquez, Juan J. L., Author
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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 Abstract: The Vlasov-Poisson system describes interacting systems of collisionless particles. For solutions with small initial data in three dimensions it is known that the spatial density of particles decays like $t^{-3}$ at late times. In this paper this statement is refined to show that each derivative of the density which is taken leads to an extra power of decay so that in $N$ dimensions for $N\ge 3$ the derivative of the density of order $k$ decays like $t^{-N-k}$. An asymptotic formula for the solution at late times is also obtained.

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 Dates: 2011
 Publication Status: Published in print
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 Identifiers: eDoc: 281819
DOI: 10.1007/s00205-011-0405-3
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Title: Archive for Rational Mechanics and Analysis
Source Genre: Journal
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Pages: - Volume / Issue: 200 (1) Sequence Number: - Start / End Page: 313 - 360 Identifier: -