GLOBAL SOLUTION FOR THE SPATIALLY INHOMOGENEOUS NON-CUTOFF KAC EQUATION

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)4503-4562
Journal / PublicationSIAM Journal on Mathematical Analysis
Volume50
Issue number4
Online published30 Aug 2018
Publication statusPublished - 2018

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Abstract

This paper is concerned with the Cauchy problem on the one-dimensional inhomogeneous non-cutoff Kac equation. Based on the analysis on the linearized operator obtained in [N. Lerner, Y. Morimoto, K. Pravda-Starov, and C.-J. Xu, J. Funct. Anal., 269 (2015), pp. 459-535], we first prove the existence of a global solution to the equation around a global Maxwellian by combining two sets of macro-micro decomposition. Then by using the dissipative norm of the linearized operator in the fractional Hermite-Sobolev space and using the perturbation theory, the spectrum structure of the linearized Kac equation is given. Based on this, the optimal time decay estimate for the nonlinear Kac equation is obtained.

Research Area(s)

  • non-cutoff Kac equation, global existence, large time behavior, LARGE-TIME BEHAVIOR, BOLTZMANN-EQUATION, WHOLE SPACE, ANGULAR CUTOFF, STRICT POSITIVITY, MAXWELLIAN GAS, EQUILIBRIUM, REGULARITY, PROPAGATION, INEQUALITY

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