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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series A Année : 2013

Strong solutions to the equations of flow and heat transfer in magnetic fluids with internal rotations

Résumé

In this paper we study the equations of flow and heat transfer in a magnetic fluid with internal rotations, when the fluid is subjected to the action of an external magnetic field. The system of equations is a combination of the Navier-Stokes equations, the magnetization relaxation equation of Bloch type, the magnetostatic equations and the temperature equation. We prove the local-in-time existence of the unique strong solution to the system equipped with initial and boundary conditions and establish a blow-up criterium for strong solutions. We then prove the global-in-time existence of strong solutions, under smallness assumptions on the initial data and the external magnetic field.
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Dates et versions

hal-00794979 , version 1 (26-02-2013)

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Citer

Youcef Amirat, Kamel Hamdache. Strong solutions to the equations of flow and heat transfer in magnetic fluids with internal rotations. Discrete and Continuous Dynamical Systems - Series A, 2013, 33 (8), pp.3289-3320. ⟨10.3934/dcds.2013.33.3289⟩. ⟨hal-00794979⟩
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