Homogenization and Hydrodynamic Limit for Fermi-Dirac Statistics Coupled to a Poisson Equation

Nader Masmoudi, Mohamed Lazhar Tayeb

Research output: Contribution to journalArticle

Abstract

This paper deals with the diffusion approximation of a Boltzmann-Poisson system modeling Fermi-Dirac statistics in the presence of an extra external oscillating electrostatic potential. Here we extend the analysis done in [19] to the case of a nonlinear collision operator. In addition to the averaging lemma and control from entropy dissipation used in [19], here we use two-scale Young measures and renormalization techniques to prove the convergence. This result rigorously justifies the formal analysis of [3].

Original languageEnglish (US)
Pages (from-to)1742-1773
Number of pages32
JournalCommunications on Pure and Applied Mathematics
Volume68
Issue number10
DOIs
StatePublished - Oct 1 2015

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Averaging Lemmas
Entropy Dissipation
Young Measures
Hydrodynamic Limit
Diffusion Approximation
Formal Analysis
Poisson equation
Poisson's equation
Ludwig Boltzmann
System Modeling
Homogenization
Renormalization
Electrostatics
Justify
Paul Adrien Maurice Dirac
Siméon Denis Poisson
Entropy
Hydrodynamics
Collision
Statistics

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Homogenization and Hydrodynamic Limit for Fermi-Dirac Statistics Coupled to a Poisson Equation. / Masmoudi, Nader; Tayeb, Mohamed Lazhar.

In: Communications on Pure and Applied Mathematics, Vol. 68, No. 10, 01.10.2015, p. 1742-1773.

Research output: Contribution to journalArticle

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