分数阶不可压缩 Navier-Stokes-Coriolis 方程解的整体适定性

数学物理学报 ›› 2024, Vol. 44 ›› Issue (3): 737-745.

分数阶不可压缩 Navier-Stokes-Coriolis 方程解的整体适定性

孙小春(),吴育联^*(),徐郜婷()

西北师范大学数学与统计学院兰州 730070

收稿日期:2023-07-31 修回日期:2023-10-16 出版日期:2024-06-26 发布日期:2024-05-17
通讯作者: *吴育联，E-mail：2021212047@nwnu.edu.cn
作者简介:孙小春，E-mail：sunxiaochun@nwnu.edu.cn;|徐郜婷，E-mail：xugaoting0129@163.com
基金资助:
国家自然科学基金(11601434)

Global Well-Posedness for the Fractional Navier-Stokes Equations with the Coriolis Force

Sun Xiaochun(),Wu Yulian^*(),Xu Gaoting()

Northwest Normal University, College of Mathematics and Statistics, Lanzhou 730070

Received:2023-07-31 Revised:2023-10-16 Online:2024-06-26 Published:2024-05-17
Supported by:
NSFC(11601434)

摘要/Abstract

摘要：

该文致力于研究带 Coriolis 力的分数阶 Navier-Stokes 方程的 Cauchy 问题. 结合半群 $S$ 的 $L^p-L^q$ 及 $\dot{H}^{\frac{5}{2}-2\alpha}-L^q$ 光滑估计, 得到了带 Coriolis 力的分数阶 Navier-Stokes 方程解的整体适定性以及 $u_0$ 在齐次 Sobolev 空间 $\dot{H}_{\sigma}^{\frac{5}{2}-2\alpha}(\mathbb{R}^3)$ 足够小时的分数阶 Navier-Stokes 方程具有唯一的整体 mild 解.

关键词: 整体适定性, 分数阶 Navier-Stokes 方程, 齐次 Sobolev 空间, Coriolis 力

Abstract:

We consider the Cauchy problem of fractional Navier-Stokes equations with the Coriolis force. Combining the $L^p-L^q$ and $\dot{H}^{\frac{5}{2}-2\alpha}-L^q$ smooth estimates of semiggroup $S$, it is proved that the well-posedness of the fractional Navier-Stokes equations with the Coriolis force and these equations possess a unique global mild solution for arbitrary speed of rotation provided the initial data $u_0$ is small enough in $\dot{H}_{\sigma}^{\frac{5}{2}-2\alpha}(\mathbb{R}^3)$.

Key words: Global well-posedness, Fractional Navier-Stokes equation, Homogeneous Sobolev spaces, Coriolis force

中图分类号:

O174.2

孙小春, 吴育联, 徐郜婷. 分数阶不可压缩 Navier-Stokes-Coriolis 方程解的整体适定性[J]. 数学物理学报, 2024, 44(3): 737-745.

Sun Xiaochun, Wu Yulian, Xu Gaoting. Global Well-Posedness for the Fractional Navier-Stokes Equations with the Coriolis Force[J]. Acta mathematica scientia,Series A, 2024, 44(3): 737-745.

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