ASYMPTOTIC BEHAVIOR OF THE NONLINEAR VLASOV EQUATION WITH A SELF-CONSISTENT FORCE

被引：5

作者：

Choi, Sun-Ho ^{[1
]}

Ha, Seung-Yeal ^{[1
]}

机构：

[1] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2011年 / 43卷 / 05期

基金：

新加坡国家研究基金会;

关键词：

asymptotic completeness; self-consistent Vlasov equation; phase transition; long-ranged force; short-ranged force; scattering; DEFINED SCATTERING OPERATORS; KLEIN-GORDON EQUATIONS; POISSON SYSTEM; GLOBAL EXISTENCE; DIMENSIONS; INITIAL DATA; SPACE; PARTICLES;

D O I：

10.1137/100815098

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a critical threshold phenomenon on the L-1-asymptotic completeness for the nonlinear Vlasov equation with a self-consistent force. For a long-ranged self-consistent force, we show that the nonlinear Vlasov equation has no L-1-asymptotic completeness, which means that the nonlinear Vlasov flow cannot be approximated by the corresponding free flow in L-1-norm time-asymptotically. In contrast, for a short-ranged force, the nonlinear Vlasov flow can be approximated by the free flow time-asymptotically. Our result corresponds to the kinetic analogue of scattering results to the Schrodinger-type equations in quantum mechanics.

引用

页码：2050 / 2077

页数：28

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