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

2024/06/04 by Matt Spragge, Spragge, Matt, Weiran Sun +1
Engineering · Mathematics · Physics and Astronomy · #Lattice Boltzmann Simulation Studies #Gas Dynamics and Kinetic Theory #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2406.02813

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 \citeAlo19 from the hard potential cases to the soft ones.

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