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Global regularity for 2D fractional magneto-micropolar equations
Mathematische Zeitschrift ( IF 0.8 ) Pub Date : 2020-06-03 , DOI: 10.1007/s00209-020-02532-6
Haifeng Shang , Jiahong Wu

The magneto-micropolar equations are important models in fluid mechanics and material sciences. This paper focuses on the global regularity problem on the 2D magneto-micropolar equations with fractional dissipation. We establish the global regularity for three important fractional dissipation cases. Direct energy estimates are not sufficient to obtain the desired global a priori bounds in each case. To overcome the difficulties, we employ various technics including the regularization of generalized heat operators on the Fourier frequency localized functions, logarithmic Sobolev interpolation inequalities and the maximal regularity property of the heat operator.

中文翻译:

二维分数阶磁微极方程的全局规律

磁微极方程是流体力学和材料科学中的重要模型。本文重点研究具有分数耗散的二维磁微极方程的全局正则性问题。我们为三个重要的分数耗散情况建立了全局规律。在每种情况下,直接能量估计不足以获得所需的全局先验界限。为了克服这些困难,我们采用了各种技术,包括对傅里叶频率局部函数的广义热算子进行正则化、对数 Sobolev 插值不等式和热算子的最大正则性。
更新日期:2020-06-03
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