Methods and Applications of Analysis

Volume 14 (2007)

Number 3

Asymptotic Completeness for Relativistic Kinetic Equations with Short-range Interaction Forces

Pages: 251 – 262

DOI: http://dx.doi.org/10.4310/MAA.2007.v14.n3.a3

Authors

Seung-Yeal Ha

Yong Duck Kim

Ho Lee

Se Eun Noh

Abstract

We present an $L^1$-asymptotic completeness results for relativistic kinetic equations with short range interaction forces. We show that the uniform phase space-time bound for nonlinear terms to the relativistic nonlinear kinetic equations yields the asymptotic completeness of the relativistic kinetic equations. For this space-time bound, we employ dispersive estimates and explicit construction of a Lyapunov functional.

Keywords

Asymptotic completeness; relativistic kinetic equation; the Vlasov-Yukawa equation; the Klein-Gordon equation

2010 Mathematics Subject Classification

Primary 35L45. Secondary 70K20, 70K40.

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