Conditional integrability and stability for the homogeneous Boltzmann equation with very soft potentials

Ricardo J. Alonso; Pierre Gervais; Bertrand Lods

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arXiv · 2403.15613

Conditional integrability and stability for the homogeneous Boltzmann equation with very soft potentials

Ricardo J. Alonso·Pierre Gervais·Bertrand Lods

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Abstract

We introduce a practical criterion that justifies the propagation and appearance of $L^{p}$-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.

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Ricardo J. Alonso, Pierre Gervais, Bertrand Lods. 2024-03-22. Conditional integrability and stability for the homogeneous Boltzmann equation with very soft potentials. https://arxiv.org/abs/2403.15613

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