Rigorous derivation of the Landau equation in the weak coupling limit
Name
Kirkpatrick-2009-RIGOROUS DERIVATION OF THE LANDAU EQUATION.pdf
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282.57 KB
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Author(s)
Kirkpatrick, Kay
Date Issued
November 2009
Journal
Communications on Pure and Applied Analysis
Publisher
American Institute of Mathematical Sciences
Citation
Kirkpatrick, Kay. “Rigorous Derivation of the Landau Equation in the Weak Coupling Limit.” Communications on Pure and Applied Analysis 8.6 (2009): 1895–1916. Web.© American Institute of Mathematical Sciences.
Version
Final published version
Abstract
We examine a family of microscopic models of plasmas, with a parameter [\alpha] comparing the typical distance between collisions to the strength of the grazing collisions. These microscopic models converge in distribution, in the weak coupling limit, to a velocity diffusion described by the linear Landau equation (also known as the Fokker-Planck equation). The present work extends and unifies previous results that handled the extremes of the parameter [alpha] to the whole range [(0,1 over 2]] ,by showing that clusters of overlapping obstacles are negligible in the limit. Additionally, we study the diffusion coefficient of the Landau equation and show it to be independent of the parameter.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.3934/cpaa.2009.8.1895
