三维不可压磁流体力学方程弱解正则准则
Regularity Criterion of the Weak Solution for the 3D Incompressible MHD Equations
DOI: 10.12677/PM.2021.114077, PDF,    科研立项经费支持
作者: 李天理：安徽职业技术学院基础教学部，安徽 合肥；王 力：安徽职业技术学院铁道学院，安徽 合肥
关键词: MHD方程；正则准则；Sobolev嵌入不等式；Young不等式；MHD Equation； Regularity Criterion； Sobolev Embedding Inequality； Young Inequality
摘要: 文章考虑在三维情况下不可压的磁流体力学(MHD)方程解的正则性。使用Young不等式，Hölder不等式及Sobolev嵌入技术等，扩大了弱解正则的函数空间，证明了当∂3u,∂3b∈Lp(0,T;Lq(R3))，2/p+3/q=46/25+3/25q, 31/8≤q≤∞时，或者当∂3u,∂3b∈Lp(0,T;Lq(R3))，2/p+3/q=22/13+3/13q,19/8≤q≤∞时，且都有，则三维不可压MHD方程弱解(u, b)在(0,T]上是正则的。
Abstract: This paper considers the regularity of weak solutions for incompressible MHD equations in 3D cases. Here, Yuong inequalities, Hölder inequalities and Sobolev embedding techniques are used to expand the integral space to which the weak solution belongs. Here, it is proved that the weak solution (u, b) is regular on (0,T], if ∂3u,∂3b∈Lp(0,T;Lq(R3)) and 2/p+3/q=46/25+3/25q, 31/8≤q≤∞ or ∂3u,∂3b∈Lp(0,T;Lq(R3)), 2/p+3/q=22/13+3/13q, 19/8≤q≤∞ ,together with .
文章引用：李天理, 王力. 三维不可压磁流体力学方程弱解正则准则[J]. 理论数学, 2021, 11(4): 640-646. https://doi.org/10.12677/PM.2021.114077

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