On a heated incompressible magnetic fluid model

Youcef Amirat (1) , Kamel Hamdache (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

In this paper we study the equations describing the dynamics of heat transfer in an incompressible magnetic fluid under the action of an applied magnetic field. The system consists of the Navier-Stokes equations, the magnetostatic equations and the temperature equation. We prove global-in-time existence of weak solutions to the system posed in a bounded domain of R-3 and equipped with initial and boundary conditions. The main difficulty comes from the singularity of the term representing the Kelvin force due to magnetization.

Mots clés: Magnetic fluid; heat transfer; incompressible flow; Navier-Stokes equations; global weak solutions.; global weak solutions

Domaines: Equations aux dérivées partielles [math.AP]

Youcef Amirat, Kamel Hamdache. On a heated incompressible magnetic fluid model. Communications on Pure and Applied Mathematics, 2011, 11 (2), pp.675 - 696. ⟨10.3934/cpaa.2012.11.675⟩. ⟨hal-00697703⟩