Journal of Mathematical Fluid Mechanics

, Volume 10, Issue 3, pp 326–351

Global Weak Solutions to Equations of Motion for Magnetic Fluids

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

Copyright information

© Birkhaueser 2007

Authors and Affiliations

  • Youcef Amirat
    • 1
  • Kamel Hamdache
    • 2
  • François Murat
    • 3
  1. 1.Laboratoire de Mathématiques, CNRS UMR 6620Université Blaise PascalAubière cedexFrance
  2. 2.Centre de Mathématiques Appliquées, CNRS UMR 7641École PolytechniquePalaiseau cedexFrance
  3. 3.Laboratoire Jacques-Louis Lions, CNRS UMR 7641Université Pierre et Marie Curie, Paris VIParis cedex 05France