不可压缩磁流体方程组在Besov空间中的爆破准则

摘要/Abstract

摘要：

该文给出了三维不可压缩磁流体（MHD）方程组在带有负指数的非齐次Besov空间中的爆破准则.结果表明方程组的经典解存在时间有限当且仅当范数‖·‖_{V_Θ}趋于无穷，这里所定义的范数‖·‖_{V_Θ}比非齐次Besov空间中的范数‖·‖_{B_∞，∞^α-1}弱，其中0 ＜ α < 1.

关键词: 不可压缩MHD方程组, 非齐次Besov空间, 爆破准则

Abstract:

In this paper, we study the blow-up criterion of smooth solutions to the threedimensional incompressible magnetohydrodynamic(MHD) equations in Besov space of negative regular index. We show that a smooth solution breaks down if and only if the certain norm of the velocity u blows up at the same time. Here the norm‖·‖_{V_Θ} is defined in nonhomogenous Besov space and it is weaker than‖·‖_{B_{∞, ∞}^α-1}-norm, for 0 < α < 1.

Key words: Incompressible MHD equations, Blow-up criterion, Besov space

中图分类号:

O175.2

尚朝阳. 不可压缩磁流体方程组在Besov空间中的爆破准则[J]. 数学物理学报, 2019, 39(1): 67-80.

Zhaoyang Shang. Blow-Up Criterion for Incompressible Magnetohydrodynamics Equations in Besov Space[J]. Acta mathematica scientia,Series A, 2019, 39(1): 67-80.

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