Time-periodic forcing and asymptotic stability for the Navier Stokes Maxwell equations

TL;DR

This paper investigates the existence and stability of small time-periodic solutions to the 3D Navier-Stokes-Maxwell equations under external periodic forcing, introducing new spaces to analyze decay over time.

Contribution

It establishes the existence and asymptotic stability of time-periodic solutions for the Navier-Stokes-Maxwell system with external forcing, using novel functional spaces.

Findings

Existence of small time-periodic solutions

Asymptotic stability of these solutions

Introduction of new spaces for decay analysis

Abstract

For the 3D Navier-Stokes-Maxwell problem on the whole space and in the presence of external time-periodic forces, first we study the existence of time-periodic small solutions, and then we prove their asymptotic stability. We use new type of spaces to account for averaged decay in time.