Journal of Mathematical Fluid Mechanics

, Volume 10, Issue 3, pp 326–351

Global Weak Solutions to Equations of Motion for Magnetic Fluids

Authors

    • Laboratoire de Mathématiques, CNRS UMR 6620Université Blaise Pascal
  • Kamel Hamdache
    • Centre de Mathématiques Appliquées, CNRS UMR 7641École Polytechnique
  • François Murat
    • Laboratoire Jacques-Louis Lions, CNRS UMR 7641Université Pierre et Marie Curie, Paris VI
Article

DOI: 10.1007/s00021-006-0234-6

Cite this article as:
Amirat, Y., Hamdache, K. & Murat, F. J. math. fluid mech. (2008) 10: 326. doi:10.1007/s00021-006-0234-6

Abstract.

We study the differential system governing the flow of an incompressible ferrofluid under the action of a magnetic field. The system consists of the Navier–Stokes equations, the angular momentum equation, the magnetization equation, and the magnetostatic equations. We prove, by using the Galerkin method, a global in time existence of weak solutions with finite energy of an initial boundary-value problem and establish the long-time behavior of such solutions. The main difficulty is due to the singularity of the gradient magnetic force.

Keywords.

Magnetic fluid flowNavier–Stokes equationsmagnetizationangular momentumweak solutions

Mathematics Subject Classification (2000).

35Q3576D05
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Copyright information

© Birkhaueser 2007