Journal of Mathematical Fluid Mechanics

, Volume 10, Issue 3, pp 326–351

Global Weak Solutions to Equations of Motion for Magnetic Fluids


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


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.


Magnetic fluid flowNavier–Stokes equationsmagnetizationangular momentumweak solutions

Mathematics Subject Classification (2000).


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