Strong solutions to the equations of electrically conductive magnetic fluids

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:421

Article

Amirat, Youcef¹  Hamdache, Kamel^2,3 

[1] Univ Clermont Ferrand 2, CNRS UMR 6620, Math Lab, F-63177 Aubiere, France

[2] Ecole Polytech, CNRS, Ctr Math Appliquees, F-91128 Palaiseau, France

[3] ECE Paris, Ecole Ingn, F-75725 Paris 15, France

关键词: Magnetic fluid;    Navier-Stokes equations;    Magnetization relaxation equation;    Induction equation;    Strong solution;    Blow-up criterion;   

DOI  :  10.1016/j.jmaa.2014.06.073

来源: Elsevier

【 摘 要 】

We study the equations of flow of an electrically conductive magnetic fluid, when the fluid is subjected to the action of an external applied magnetic field. The system is formed by the incompressible Navier-Stokes equations, the magnetization relaxation equation of Bloch type and the magnetic induction equation. The system takes into account the Kelvin and Lorentz force densities. We prove the local-in-time existence of the unique strong solution to the system equipped with initial and boundary conditions. We also establish a blow-up criterion for the local strong solution. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free