Global analysis for strong solutions to the equations of a ferrofluid flow model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:364

Article

Tan, Zhong¹  Wang, Yanjin¹ 

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China

关键词: Ferrohydrodynamics;    Magnetic;    Navier-Stokes equations;    Strong solutions;    Decay rate;   

DOI  :  10.1016/j.jmaa.2009.10.032

来源: Elsevier

【 摘 要 】

In this paper we are concerned with the differential system proposed by Shliomis to describe the motion of an incompressible ferrofluid submitted to an external magnetic field. The system consists of the Navier-Stokes equations, the magnetization equations and the magnetostatic equations. No regularizing term is added to the magnetization equations. We prove the local existence of unique strong solution for the Cauchy problem and establish a finite time blow-up criterion of strong solutions. Under the smallness assumption of the initial data and the external magnetic field, we prove the global existence of strong solutions and derive a decay rate of such small solutions in L-2-norm. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free