A weak- $$L^{p}$$ Prodi–Serrin type regularity criterion for the micropolar fluid equations in terms of the pressure

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-12-15 DOI:10.1007/s11587-023-00829-2

Ines Ben Omrane, Mourad Ben Slimane, Sadek Gala, Maria Alessandra Ragusa

引用次数: 0

Abstract

This paper is devoted to investigating regularity criteria for the 3D micropolar fluid equations in terms of pressure in weak Lebesgue space. More precisely, we mainly proved that the weak solution is regular on (0, T] provided that either the norm $\left\| \pi \right\| _{L^{\alpha ,\infty }(0,T;L^{\beta ,\infty }(\mathbb {R}^{3}))}$ with $\frac{2}{\alpha }+ \frac{3}{\beta }=2$ and $\frac{3}{2}<\beta <\infty $ or $\left\| \nabla \pi \right\| _{L^{\alpha ,\infty }(0,T;L^{\beta ,\infty }(\mathbb {R} ^{3}))}$ with $\frac{2}{\alpha }+\frac{3}{\beta }=3$ and $1<\beta <\infty $ is sufficiently small.

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用压力表示的微极性流体方程的弱$L^{p}$$Prodi-Serrin 型正则准则

本文致力于研究三维微波流体方程在弱 Lebesgue 空间中的正则性准则。更确切地说，我们主要证明了弱解在 (0, T] 上是正则的，条件是规范 $\left\| \pi \right\| _{L^{\alpha ,\infty }(0,T.)；L^{beta ,\infty }(\mathbb {R}^{3}))}$ with $\frac{2}{alpha }+ \frac{3}{beta }=2$ and$\frac{3}{2}<；\beta <\infty $ or$\left\| \nabla \pi \right\| _{L^{\alpha ,\infty }(0,T.)) 和L^{beta ,\infty }(\mathbb {R} ^{3}))}$ with $\frac{2}{alpha }+\frac{3}{beta }=3$ and$1<\beta <\infty$ is sufficiently small.

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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