Spatial behavior of the solution to the linearized Boltzmann equation with hard potentials

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Abstract

The main goal is to understand the quantitative spatial decay of the solution to the linearized Boltzmann equation for hard potentials with cutoff. We obtain the quantitative space-time behavior of the linearized Boltzmann equation under some slow velocity decay assumption but without any regularity assumption on the initial data. This result extends the classical results of Liu and Yu [Commun. Pure Appl. Math. 57, 1543-1608 (2004); Bull. Inst. Math. Acad. Sin. 1, 1-78 (2006); and ibid. 6, 151-243 (2011)] from hard sphere to hard potential under the same assumption on the initial condition [compactly support in the space variable and polynomial decay in the velocity variable with power β = (3/2)+].

Original languageEnglish
Article number021504
JournalJournal of Mathematical Physics
Volume61
Issue number2
DOIs
Publication statusPublished - 2020 Feb 1

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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