Global solutions of the Euler-Maxwell two-fluid system in 3D
type: Item
instance of: scholarly article
title: Global solutions of the Euler-Maxwell two-fluid system in 3D
zbMATH Open document ID: 1345.35075
author: Yan Guo
author: Benoit Pausader
author: Alexandru D. Ionescu
published in: Annals of Mathematics. Second Series
publication date: 2016-04-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/1303.1060
review text: The results obtained in this article are related to the Euler-Maxwell system, that represents the two-fluid model describing plasma dynamics. This model is a system of nonlinear hyperbolic conservation laws with no dissipation and no relaxation effects. The authors develop a method that can be used for complicated physical coupled systems, at least in dimension 3. The global dynamics of the solutions to the Euler-Maxwell system is analyzed by means of dispersive analysis combined with energy estimates, relying on the Fourier transform. It is proved that irrotational, smooth and localized perturbations of a constant background with small amplitude lead to global smooth solutions for the 3D Euler-Maxwell system. The proposed method can be extended to other quasilinear problems in 3D and the constructed solutions represent the first smooth, nontrivial global solutions.
reviewed by: Ruxandra Stavre
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76X05
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 6575342
zbMATH Keywords: dispersive analysis
zbMATH Keywords: Euler-Maxwell two-fluid model
zbMATH Keywords: global regularity
zbMATH Keywords: space-time resonances
zbMATH Keywords: the Fourier transform method
MaRDI profile type: Publication
OpenAlex ID: W2233368132
arXiv ID: 1303.1060
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DOI: 10.4007/ANNALS.2016.183.2.1
description: scientific article; zbMATH DE number 6575342