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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.|
|Electronic Publication Date:||13-Apr-2017|
|Citation:||Deng, Yu, Ionescu, Alexandru D, Pausader, Benoit. (2017). The Euler-Maxwell System for Electrons: Global Solutions in 2D. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 225 (771 - 871. doi:10.1007/s00205-017-1114-3|
|Pages:||771 - 871|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS|
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