$L^p$-norms for the homogeneous non-cutoff Boltzmann equation with soft potentials

Matt Spragge; Weiran Sun

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arXiv · 2406.02813

$L^p$-norms for the homogeneous non-cutoff Boltzmann equation with soft potentials

Matt Spragge·Weiran Sun

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Abstract

We establish a priori estimates showing the propagation and generation of $L^p$-norms for solutions to the non-cutoff spatially homogeneous Boltzmann equation with soft potentials. The singularity of the collision kernel is key to generate regularization and inhomogeneity in the energy estimates of the $L^p$-norms. Our result extends \cite{Alo19} from the hard potential cases to the soft ones.

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Matt Spragge, Weiran Sun. 2024-06-04. $L^p$-norms for the homogeneous non-cutoff Boltzmann equation with soft potentials. https://arxiv.org/abs/2406.02813

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