REGULARITY OF WEAK SOLUTIONS TO MAGNETO-MICROPOLAR FLUID EQUATIONS

doi:10.1016/S0252-9602(10)60139-7

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (5): 1469-1480.doi: 10.1016/S0252-9602(10)60139-7

REGULARITY OF WEAK SOLUTIONS TO MAGNETO-MICROPOLAR FLUID EQUATIONS

原保全

School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454000, China

收稿日期:2008-09-24 出版日期:2010-09-20 发布日期:2010-09-20
基金资助:
The author was partially supported by the National Natural Science Foundation of China (10771052), Program for Science \& Technology Innovation Talents in Universities of Henan Province (2009HASTIT007), Doctor Fund of Henan Polytechnic University (B2008-62), and Innovation Scientists and Technicians Troop Construction Projects of Henan Province.

REGULARITY OF WEAK SOLUTIONS TO MAGNETO-MICROPOLAR FLUID EQUATIONS

YUAN Bao-Quan

School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454000, China

Received:2008-09-24 Online:2010-09-20 Published:2010-09-20
Supported by:
The author was partially supported by the National Natural Science Foundation of China (10771052), Program for Science \& Technology Innovation Talents in Universities of Henan Province (2009HASTIT007), Doctor Fund of Henan Polytechnic University (B2008-62), and Innovation Scientists and Technicians Troop Construction Projects of Henan Province.

摘要/Abstract

摘要：

In this article, we study the regularity of weak solutions and the blow-up criteria for smooth solutions to the magneto-micropolar fluid
equations in R³. We obtain the classical blow-up criteria for smooth solutions (u, ω,b), i.e., L^q(0,T; L^p(R³) )for 2/q+3/p≤1 with 3<p≤∞, u ∈ C([0, T); L³(R³)) or $\nabla u\in L^q(0, T; L^p) for 3/2< p ≤∞ satisfying 2/q+3/p≤2. Moreover, our results indicate that the regularity of weak solutions is dominated by the velocity u of the fluid. In the end-point case p=∞, the blow-up criteria can be extended to more general spaces $\nabla u\in L¹(0, T; B⁰_∞,_∞(R³)).

关键词: magneto-micropolar fluid equations, regularity criteria, blow-up criteria

Abstract:

Key words: magneto-micropolar fluid equations, regularity criteria, blow-up criteria

中图分类号:

35Q35

原保全. REGULARITY OF WEAK SOLUTIONS TO MAGNETO-MICROPOLAR FLUID EQUATIONS[J]. 数学物理学报(英文版), 2010, 30(5): 1469-1480.

YUAN Bao-Quan. REGULARITY OF WEAK SOLUTIONS TO MAGNETO-MICROPOLAR FLUID EQUATIONS[J]. Acta mathematica scientia,Series B, 2010, 30(5): 1469-1480.

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REGULARITY OF WEAK SOLUTIONS TO MAGNETO-MICROPOLAR FLUID EQUATIONS

REGULARITY OF WEAK SOLUTIONS TO MAGNETO-MICROPOLAR FLUID EQUATIONS

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