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Global weak solutions to a ferrofluid flow model

✍ Scribed by Youcef Amirat; Kamel Hamdache

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
282 KB
Volume
31
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We are concerned with the global solvability of the differential system introduced by Shliomis to describe the flow of a colloidal suspension of magnetized nanoparticles in a nonconducting liquid, under the action of an external magnetic field. The system is a combination of the Navier–Stokes equations, the magnetization equation, and the magnetostatic equations. We prove, by using a method of regularization, the existence of global‐in‐time weak solutions with finite energy to an initial boundary‐value problem and establish the long‐time behaviour of such solutions. The main difficulty is due to the singularity of the gradient magnetic force and the torque. Copyright Β© 2007 John Wiley & Sons, Ltd.

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