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

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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 L 2 bound on an oscillatory integral operator, and Fourier analysis of the Duhamel formula.

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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012, USA

    Yu Deng

  2. Princeton University, Princeton, NJ, USA

    Alexandru D. Ionescu

  3. Brown University, Providence, RI, 02912, USA

    Benoit Pausader

Authors
  1. Yu Deng
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  2. Alexandru D. Ionescu
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  3. Benoit Pausader
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Corresponding author

Correspondence to Alexandru D. Ionescu.

Additional information

Communicated by P. Constantin

Communicated by P. Constantin

Deng was supported in part by a Jacobus Fellowship from Princeton University. Ionescu was supported in part by NSF Grants DMS-1265818 and FRG-1463753. Pausader author was supported in part by NSF Grants DMS-1069243 and DMS-1362940, and a Sloan fellowship.

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Deng, Y., Ionescu, A.D. & Pausader, B. The Euler–Maxwell System for Electrons: Global Solutions in 2D . Arch Rational Mech Anal 225, 771–871 (2017). https://doi.org/10.1007/s00205-017-1114-3

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  • DOI: https://doi.org/10.1007/s00205-017-1114-3

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