Conditional integrability and stability for the homogeneous Boltzmann equation with very soft potentials
Analysis of PDEs
2025-06-30 v2
Abstract
We introduce a practical criterion that justifies the propagation and appearance of -norms for the solutions to the spatially homogeneous Boltzmann equation with very soft potentials without cutoff. Such criterion also provides a new conditional stability result for classical solutions to the equation. All results are quantitative. Our approach is inspired by a recent analogous result for the Landau equation derived in arXiv:2306.15729 and generalises existing conditional results related to higher integrability properties and stability of solutions to the Boltzmann equation with very soft potentials.
Cite
@article{arxiv.2403.15613,
title = {Conditional integrability and stability for the homogeneous Boltzmann equation with very soft potentials},
author = {Ricardo J. Alonso and Pierre Gervais and Bertrand Lods},
journal= {arXiv preprint arXiv:2403.15613},
year = {2025}
}
Comments
accepted for publication