The Euler–Maxwell System for Electrons: Global Solutions in 2D

Yu Deng, Alexandru D. Ionescu, Benoit Pausader

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

A basic model for describing plasma dynamics is given by the Euler–Maxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagnetic field. In this paper we consider the “one-fluid” Euler–Maxwell model for electrons, in 2 spatial dimensions, and prove global stability of a constant neutral background. In 2 dimensions our global solutions have relatively slow (strictly less than 1/t) pointwise decay and the system has a large (codimension 1) set of quadratic time resonances. The issue in such a situation is to solve the “division problem”. To control the solutions we use a combination of improved energy estimates in the Fourier space, an L2 bound on an oscillatory integral operator, and Fourier analysis of the Duhamel formula.

Original languageEnglish (US)
Pages (from-to)771-871
Number of pages101
JournalArchive for Rational Mechanics and Analysis
Volume225
Issue number2
DOIs
StatePublished - Aug 1 2017

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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