Self-generating lower bounds and continuation for the Boltzmann equation

2020/05/27 by Henderson, Christopher, Snelson, Stanley, Tarfulea, Andrei · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2005.13668

Abstract

For the spatially inhomogeneous, non-cutoff Boltzmann equation posed in the whole space \mathbb R³_x, 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.

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• Unconditional alignment of solutions to the Fokker-Planck-Navier-Stokes system with locally averaged Brinkman force

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