Titre :

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

Auteur(s) :

Alonso, Ricardo [Auteur]
Texas A&M University at Qatar
Gervais, Pierre [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Lods, Bertrand [Auteur]
Università degli studi di Torino = University of Turin [UNITO]

Date de publication :

2024

Mot(s)-clé(s) en anglais :

Boltzmann equation
Commutator estimates
ε-Poincaré inequality
Regularity theory
Uniqueness

Discipline(s) HAL :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

Résumé en anglais : [en]

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 ...
Lire la suite >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.Lire moins >

Langue :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL