# American Institute of Mathematical Sciences

March  2019, 18(2): 709-734. doi: 10.3934/cpaa.2019035

## Weak solutions to stationary equations of heat transfer in a magnetic fluid

 1 Laboratoire de Mathématiques Blaise Pascal, Université Clermont Auvergne, CNRS UMR 6620, Campus universitaire des Cézeaux, 3, place Vasarely, 63178, Aubière, France 2 Pôle universitaire Léonard de Vinci. DVRC. 92916 Paris la Défense Cedex

* Corresponding author

Received  January 2018 Revised  July 2018 Published  October 2018

We consider the differential system describing the stationary heat transfer in a magnetic fluid in the presence of a heat source and an external magnetic field. The system consists of the stationary incompressible Navier-Stokes equations, the magnetostatic equations and the stationary heat equation. We prove, for the differential system posed in a bounded domain of $\mathbb{R}^3$ and equipped with Fourier boundary conditions, the existence of weak solutions by using a regularization of the Kelvin force and the thermal power.

Citation: Youcef Amirat, Kamel Hamdache. Weak solutions to stationary equations of heat transfer in a magnetic fluid. Communications on Pure & Applied Analysis, 2019, 18 (2) : 709-734. doi: 10.3934/cpaa.2019035
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