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

Youcef Amirat (1, 2) , Kamel Hamdache (3)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 UCA [2017-2020] - Université Clermont Auvergne [2017-2020]
3 Pôle Universitaire Léonard de Vinci

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 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.

Domaines: Equations aux dérivées partielles [math.AP]

Youcef Amirat, Kamel Hamdache. Weak solutions to stationary equations of heat transfer in a magnetic fluid. Communications on Pure and Applied Analysis, 2019, 18 (2), pp.709-734. ⟨10.3934/cpaa.2019035⟩. ⟨hal-01906553⟩