Dispersion estimates for the two-dimensional Vlasov-Yukawa system with small data

Sun Ho Choi; Seung Yeal Ha; Ho Lee

doi:10.1016/j.jde.2010.10.005

Dispersion estimates for the two-dimensional Vlasov-Yukawa system with small data

Sun Ho Choi, Seung Yeal Ha, Ho Lee

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

We present dispersion estimates for the two-dimensional Vlasov-Yukawa system with small data. When the initial data are sufficiently regular and small, we show that the local mass density and the Yukawa force field decay to zero algebraically fast in time. These dispersion estimates are not known for the two-dimensional Vlasov-Poisson system. For the dispersion estimates, we effectively use the short-range character of the Yukawa potential and the optimal gradient estimates introduced by Hwang, Rendall and Velázquez for the three-dimensional Vlasov-Poisson system.

Original language	English
Pages (from-to)	515-550
Number of pages	36
Journal	Journal of Differential Equations
Volume	250
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2010.10.005
Publication status	Published - 1 Jan 2011

Bibliographical note

Funding Information:
The work of S.-H. Choi is supported by Hi Seoul Science/Humanities Fellowship from Seoul, and the work of S.-Y. Ha is supported by National Research Foundation of Korea Grant funded by the Korean Government (2009-0093137). The work of H. Lee was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (2010-0001986).

Keywords

Dispersion estimates
L1-stability
Vlasov-Yukawa system

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10.1016/j.jde.2010.10.005

Cite this

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title = "Dispersion estimates for the two-dimensional Vlasov-Yukawa system with small data",

abstract = "We present dispersion estimates for the two-dimensional Vlasov-Yukawa system with small data. When the initial data are sufficiently regular and small, we show that the local mass density and the Yukawa force field decay to zero algebraically fast in time. These dispersion estimates are not known for the two-dimensional Vlasov-Poisson system. For the dispersion estimates, we effectively use the short-range character of the Yukawa potential and the optimal gradient estimates introduced by Hwang, Rendall and Vel{\'a}zquez for the three-dimensional Vlasov-Poisson system.",

keywords = "Dispersion estimates, L1-stability, Vlasov-Yukawa system",

author = "Choi, {Sun Ho} and Ha, {Seung Yeal} and Ho Lee",

note = "Funding Information: The work of S.-H. Choi is supported by Hi Seoul Science/Humanities Fellowship from Seoul, and the work of S.-Y. Ha is supported by National Research Foundation of Korea Grant funded by the Korean Government (2009-0093137). The work of H. Lee was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (2010-0001986).",

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AU - Ha, Seung Yeal

AU - Lee, Ho

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N2 - We present dispersion estimates for the two-dimensional Vlasov-Yukawa system with small data. When the initial data are sufficiently regular and small, we show that the local mass density and the Yukawa force field decay to zero algebraically fast in time. These dispersion estimates are not known for the two-dimensional Vlasov-Poisson system. For the dispersion estimates, we effectively use the short-range character of the Yukawa potential and the optimal gradient estimates introduced by Hwang, Rendall and Velázquez for the three-dimensional Vlasov-Poisson system.

AB - We present dispersion estimates for the two-dimensional Vlasov-Yukawa system with small data. When the initial data are sufficiently regular and small, we show that the local mass density and the Yukawa force field decay to zero algebraically fast in time. These dispersion estimates are not known for the two-dimensional Vlasov-Poisson system. For the dispersion estimates, we effectively use the short-range character of the Yukawa potential and the optimal gradient estimates introduced by Hwang, Rendall and Velázquez for the three-dimensional Vlasov-Poisson system.

KW - Dispersion estimates

KW - L1-stability

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DO - 10.1016/j.jde.2010.10.005

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JO - Journal of Differential Equations

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IS - 1

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Dispersion estimates for the two-dimensional Vlasov-Yukawa system with small data

Abstract

Bibliographical note

Keywords

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