Global Weak Solutions to Equations of Motion for Magnetic Fluids
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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.
Keywords.Magnetic fluid flow Navier–Stokes equations magnetization angular momentum weak solutions
Mathematics Subject Classification (2000).35Q35 76D05
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