Self-generating lower bounds and continuation for the Boltzmann equation
AffiliationUniv Arizona, Dept Math
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CitationHenderson, C., Snelson, S. & Tarfulea, A. Self-generating lower bounds and continuation for the Boltzmann equation. Calc. Var. 59, 191 (2020). https://doi.org/10.1007/s00526-020-01856-9
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AbstractFor the spatially inhomogeneous, non-cutoff Boltzmann equation posed in the whole space R-x(3), 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.
Note12 month embargo; published 13 October 2020
VersionFinal accepted manuscript