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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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