Global existence for the Euler-Maxwell system

TL;DR

This paper proves the global existence of small solutions to the three-dimensional Euler-Maxwell system, a model for plasma dynamics, using advanced analytical techniques to handle slow decay and derivative growth.

Contribution

It introduces a novel approach combining space-time resonance, dispersive, localization, and energy estimates to establish global solutions with slow derivative growth.

Findings

Global existence of small solutions in 3D space

Handling of nonintegrable decay with slow derivative growth

Application of combined analytical methods for complex PDE systems

Abstract

The Euler-Maxwell system describes the evolution of a plasma when the collisions are important enough that each species is in a hydrodynamic equilibrium. In this paper we prove global existence of small solutions to this system set in the whole three-dimensional space, by combining the space-time resonance method, dispersive estimates, localization estimates and energy estimates. An important novelty is that we can prove a very slow growth of high derivatives even with a nonintegrable decay by reiterating the energy estimate.