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Green's Function of Boltzmann Equation, 3-D Waves
by Tai-Ping Liu   Shih-Hsien Yu

Vol. 1 No. 1 (2006) P.1~P.78

ABSTRACT

We study the Green's function for the linearized Boltzmann equation. For the short-time period, the Green's function is dominated by the particle-like waves; and for large-time, by the fluid-like waves exhibiting the weak Huygens principle. The fluid-like waves are constructed by the spectral analysis and complex analytic techniques, making uses of the rotational symmetry of the equation in the space variables. The particle-like waves are constructed by a Picard iteration, making uses of the exchange of regularity in the microscopic velocity with the regularity in the space variables through a Mixture Lemma. We obtain the pointwise estimates in the space and time variables of the Green's function through a long-short waves and particle-wave decompositions.

KEYWORDS
Boltzmann equation, Green's function, Mixture Lemma, particle- uid waves, weak Huygens principle

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 76P05, 35L65, 82C40

MILESTONES