TY - JOUR

T1 - The Euler–Maxwell System for Electrons

T2 - Global Solutions in 2D

AU - Deng, Yu

AU - Ionescu, Alexandru D.

AU - Pausader, Benoit

N1 - Funding Information:
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.
Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.

PY - 2017/8/1

Y1 - 2017/8/1

N2 - 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.

AB - 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.

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U2 - 10.1007/s00205-017-1114-3

DO - 10.1007/s00205-017-1114-3

M3 - Article

AN - SCOPUS:85017451895

VL - 225

SP - 771

EP - 871

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 2

ER -