Space-time behavior of the solution to the Boltzmann equation with soft potentials

Yu Chu Lin, Ming Jiea Lyu, Haitao Wang, Kung Chien Wu

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this paper, we get the quantitative space-time behavior of the full Boltzmann equation with soft potentials (−2<γ<0) in the close to equilibrium setting, under some velocity decay assumption, but without any Sobolev regularity assumption on the initial data. We find that both the large time and spatial behaviors depend on the velocity decay of the initial data and the exponent γ. The key step in our strategy is to obtain the L bound of a suitable weighted full Boltzmann equation directly, rather than using Green's function and Duhamel's principle to construct the pointwise structure of the solution as in [25]. This provides a new thinking in the related study.

Original languageEnglish
Pages (from-to)180-236
Number of pages57
JournalJournal of Differential Equations
Volume322
DOIs
Publication statusPublished - 2022 Jun 15

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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