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

Youcef Amirat; Kamel Hamdache

doi:10.3934/cpaa.2019035

Article Contents

2019, Volume 18, Issue 2: 709-734. Doi: 10.3934/cpaa.2019035

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

Youcef Amirat^1, , and
Kamel Hamdache^2,

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
* Corresponding author

Received: January 2018

Revised: July 2018

Published: October 2018

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q35, 76D05.

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References

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