### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 771-871 |

Number of pages | 101 |

Journal | Archive for Rational Mechanics and Analysis |

Volume | 225 |

Issue number | 2 |

DOIs | |

State | Published - Aug 1 2017 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering

## Fingerprint Dive into the research topics of 'The Euler–Maxwell System for Electrons: Global Solutions in 2D'. Together they form a unique fingerprint.

## Cite this

*Archive for Rational Mechanics and Analysis*,

*225*(2), 771-871. https://doi.org/10.1007/s00205-017-1114-3