Global Weak Solutions to Equations of Motion for Magnetic Fluids
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- Amirat, Y., Hamdache, K. & Murat, F. J. math. fluid mech. (2008) 10: 326. doi:10.1007/s00021-006-0234-6
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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.