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Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type , Journal 20 Mar 2006Embargo end date: 23 Apr 2018 United Kingdom, France Publisher:IOP PublishingJournal:Nonlinearity, volume 19, pages 969-998 (issn: 0951-7715, eissn: 1361-6544,

Authors: Mouhot, Clément; Neumann, Lukas;

doi: 10.1088/0951-7715/19/4/011 , 10.17863/cam.22297 , 10.48550/arxiv.math/0607530

arXiv: http://arxiv.org/abs/math/0607530 , math/0607530

Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus

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Abstract

For a general class of linear collisional kinetic models in the torus, including in particular the linearized Boltzmann equation for hard spheres, the linearized Landau equation with hard and moderately soft potentials and the semi-classical linearized fermionic and bosonic relaxation models, we prove explicit coercivity estimates on the associated integro-differential operator for some modified Sobolev norms. We deduce existence of classical solutions near equilibrium for the full non-linear models associated, with explicit regularity bounds, and we obtain explicit estimates on the rate of exponential convergence towards equilibrium in this perturbative setting. The proof are based on a linear energy method which combines the coercivity property of the collision operator in the velocity space with transport effects, in order to deduce coercivity estimates in the whole phase space.

Countries

United Kingdom, France

Related Organizations

Centre De Recherche en Mathématiques de la Décision
France
University of Paris
France
Paris Dauphine University
France
Austrian Academy of Sciences
Austria
Johann Radon Institute for Computational and Applied Mathematics
Austria

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Keywords

BOUNDS, MAXWELLIANS, explicit, FOS: Physical sciences, 530, semi-classical relaxation, 510, 519, Boltzmann equation, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics - Analysis of PDEs, relaxation, bosons, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], collisional kinetic models, fermions, HOMOGENEOUS BOLTZMANN-EQUATION, FOS: Mathematics, FOKKER-PLANCK EQUATION, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Landau equation, 76P05 Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05], Mathematical Physics, TREND, GLOBAL EQUILIBRIUM, weak external field, [ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph], rate of convergence to equilibrium, energy method, BOSE-EINSTEIN PARTICLES, Mathematical Physics (math-ph), Probabilités et mathématiques appliquées, TIME, [MATH.MATH-AP] Mathematics/Analysis of PDEs, [MATH.MATH-MP] Mathematics/Mathematical Physics, Fokker-Planck, Poisson self-consistent potential, CLASSICAL-SOLUTIONS, SYSTEM, Analysis of PDEs (math.AP)

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	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 1%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Top 10%