Global weak solutions to magnetic fluid flows with nonlinear Maxwell-Cattaneo heat transfer law

Fatah Aggoune (1) , Kamel Hamdache (2) , Djamila Hamroun (1)

1 AMNEDP - Laboratoire AMNEDP, Faculté de Mathématiques, Université USTHB, Algérie
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We discuss the equations describing the dynamic of the heat transfer in a magnetic fluid flow under the action of an applied magnetic field. Instead of the usual heat transfer equation we use a generalization given by the Maxwell-Cattaneo law which is a system satisfied by the temperature and the heat flux. We prove a global existence of weak solutions to the system having a finite energy.

Mots clés: Navier-Stokes equations; Bloch-Torrey equation; magnetostatic equation; Maxwell-Cattaneo law; heat transfer; magnetic field; magnetization

Domaines: Equations aux dérivées partielles [math.AP]

Fatah Aggoune, Kamel Hamdache, Djamila Hamroun. Global weak solutions to magnetic fluid flows with nonlinear Maxwell-Cattaneo heat transfer law. 2014. ⟨hal-01023053⟩