Conditional integrability and stability ...
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Pré-publication ou Document de travail
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Title :
Conditional integrability and stability for the homogeneous Boltzmann equation with very soft potentials
Author(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]
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]
Publication date :
2024
English keyword(s) :
Boltzmann equation
Commutator estimates
ε-Poincaré inequality
Regularity theory
Uniqueness
Commutator estimates
ε-Poincaré inequality
Regularity theory
Uniqueness
HAL domain(s) :
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
English abstract : [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 ...
Show more >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.Show less >
Show more >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.Show less >
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Anglais
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Submission date :
2025-01-24T11:14:39Z
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