Time-periodic solutions to heated ferrofluid flow 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.