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 language||English (US)|
|Journal||Calculus of Variations and Partial Differential Equations|
|State||Published - Dec 1 2020|
ASJC Scopus subject areas
- Applied Mathematics