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磁微极流体方程在临界Sobolev空间解的渐进性质
供稿: 原保全;马丽 时间: 2018-11-26 次数:

作者:原保全马丽

作者单位:河南理工大学数学与信息科学学院

摘要:运用能量估计的方法,在临界Sobolev空间H1/2(R3)中,研究了三维不可压磁微极流体方程小初值整体强解的渐进性质.设(u,ω,b)是三维不可压磁微极流体方程在临界Sobolev空间H1/2(R3)中小初值(u0,ω0,b0)∈H1/2(R3)对应的整体强解,那么解的H1/2(R3)范数‖u,ω,b‖H1/2关于时间t是非增函数,且当t→+∞时,极限为0;并且使得整体强解(u,ω,b)存在的小初值(u0,ω0,b0)构成的集合是空间H1/2(R3)中的开集.

基金:国家自然科学基金资助项目(11071057);河南省杰出青年计划项目(104100510015);

关键词:磁微极流体方程;临界Sobolev空间;强解;渐进性质;

DOI:10.16186/j.cnki.1673-9787.2013.06.001

分类号:O175;O357

Abstract:By virtue of the energy estimating method, the asymptotic properties of the global strong solution for the 3D incompressible magneto-micropolar fluid equations with small initial data are showed. Suppose that ( u, ω, b) is a global strong solution to the system with small initial data ( u 0, ω 0, b 0) , then ‖ ( u, ω, b) ‖H1/2is nonincreasing for the time and when t→ + ∞, ‖ ( u, ω, b) ‖H1/2 →0; The set of small initial data ( u0, ω 0, b 0) such as the global strong solutions ( u, ω, b) existing in a system is an open subset inH1 2 ( R3) .

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