Self-generating lower bounds and continuation for the Boltzmann equation

Christopher Henderson, Stanley Snelson, Andrei Tarfulea

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

For the spatially inhomogeneous, non-cutoff Boltzmann equation posed in the whole space Rx3, we establish pointwise lower bounds that appear instantaneously even if the initial data contains vacuum regions. Our lower bounds depend only on the initial data and upper bounds for the mass and energy densities of the solution. As an application, we improve the weakest known continuation criterion for large-data solutions, by removing the assumptions of mass bounded below and entropy bounded above.

Original languageEnglish (US)
Article number191
JournalCalculus of Variations and Partial Differential Equations
Volume59
Issue number6
DOIs
StatePublished - Dec 1 2020
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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