Asymptotic of grazing collisions for the spatially homogeneous Boltzmann equation for soft and Coulomb potentials

Autor: David Godinho
Přispěvatelé: Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), Godinho, David, Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)
Rok vydání: 2012
Předmět:
Statistics and Probability
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]
Quadratic cost
Mathematics Subject Classification (2000): 82C40
60K35
FOS: Physical sciences
01 natural sciences
Boltzmann equation
010104 statistics & probability
symbols.namesake
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]
Coulomb
FOS: Mathematics
Limit (mathematics)
[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]
0101 mathematics
Kinetic Theory
Landau equation
Mathematical Physics
Mathematical physics
Mathematics
Applied Mathematics
010102 general mathematics
Probability (math.PR)
Grazing collisions
Mathematical Physics (math-ph)
Condensed Matter::Mesoscopic Systems and Quantum Hall Effect
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
Rate of convergence
Homogeneous
Modeling and Simulation
Boltzmann constant
symbols
Kinetic theory of gases
Mathematics - Probability
76P05
82C40
DOI: 10.48550/arxiv.1212.4971
Popis: We give an explicit bound for the Wasserstein distance with quadratic cost between the solutions of Boltzmann's and Landau's equations in the case of soft and Coulomb potentials. This gives an explicit rate of convergence for the grazing collisions limit. Our result is local in time for very soft and Coulomb potentials and global in time for moderately soft potentials.
Comment: 52 pages
Databáze: OpenAIRE
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