Time-periodic solutions to heated ferrofluid flow models

TL;DR

This paper proves the existence of time-periodic solutions in a coupled ferrofluid flow model involving Navier-Stokes, temperature, and magnetostatic equations, with a non-linear magnetization law.

Contribution

It introduces a novel proof of time-periodic solutions for a complex ferrofluid model with non-linear magnetization, using semi-Galerkin and fixed point methods.

Findings

Existence of time-periodic solutions established

Coupled PDE system with non-linear magnetization analyzed

Methodology applicable to similar ferrofluid models

Abstract

In this work we prove the existence of time-periodic solutions to a model describing a ferrofluid flow heated from below. Navier-Stokes equations satisfied by the fluid velocity are coupled to the temperature equation and the magnetostatic equation satisfied by the magnetic potential. The magnetization is assumed to be parallel to the magnetic field and is given by a non-linear magnetization law generalizing the Langevin law. The proof is based on a semi-Galerkin approximation and regularization methods together with the fixed point method.