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Publication details

Document type
Journal articles

Document subtype
Full paper

Title
On Strong Convergence to Equilibrium for the Boltzmann Equation with Soft Potentials

Participants in the publication
Eric A. Carlen (Author)
RUTGERS UNIVERSITY
Maria C. Carvalho (Author)
Dep. Matemática
CMAF - Centro de Matemática e Aplicações Fundamentais 
Xuguang Lu (Author)

Scope
International

Refereeing
Yes

Summary
The paper concerns L 1-convergence to equilibrium for weak solutions of the spatially homogeneous Boltzmann Equation for soft potentials (−4≤γ<0), with and without angular cutoff. We prove the time-averaged L 1-convergence to equilibrium for all weak solutions whose initial data have finite entropy and finite moments up to order greater than 2+|γ|. For the usual L 1-convergence we prove that the convergence rate can be controlled from below by the initial energy tails, and hence, for initial data with long energy tails, the convergence can be arbitrarily slow. We also show that under the integrable angular cutoff on the collision kernel with −1≤γ<0, there are algebraic upper and lower bounds on the rate of L 1-convergence to equilibrium. Our methods of proof are based on entropy inequalities and moment estimates.

Date of Submisson/Request
2008-08-07
Date of Acceptance
2009-04-08
Date of Publication
2009-05

Where published
Journal of Statistical Physics

Publication Identifiers
ISSN - 0022-4715,1572-9613

Publisher
Springer Science and Business Media LLC

Volume
135
Number
4

Number of pages
55
Starting page
681
Last page
736

Document Identifiers
DOI - https://doi.org/10.1007/s10955-009-9741-1
URL - http://dx.doi.org/10.1007/s10955-009-9741-1

Tags
Boltzmann equation Soft potentials Weak solutions Strong convergence Equilibrium


Export

APA
Eric A. Carlen, Maria C. Carvalho, Xuguang Lu, (2009). On Strong Convergence to Equilibrium for the Boltzmann Equation with Soft Potentials. Journal of Statistical Physics, 135, 681-736. ISSN 0022-4715,1572-9613. eISSN . http://dx.doi.org/10.1007/s10955-009-9741-1

IEEE
Eric A. Carlen, Maria C. Carvalho, Xuguang Lu, "On Strong Convergence to Equilibrium for the Boltzmann Equation with Soft Potentials" in Journal of Statistical Physics, vol. 135, pp. 681-736, 2009. 10.1007/s10955-009-9741-1

BIBTEX
@article{44958, author = {Eric A. Carlen and Maria C. Carvalho and Xuguang Lu}, title = {On Strong Convergence to Equilibrium for the Boltzmann Equation with Soft Potentials}, journal = {Journal of Statistical Physics}, year = 2009, pages = {681-736}, volume = 135 }