三维不可压Navier-Stokes方程组轨道统计解的退化正则性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (2): 336-344.

三维不可压Navier-Stokes方程组轨道统计解的退化正则性

徐明月¹(),赵才地^1,*(),TomásCaraballo²()

¹ 温州大学数理学院浙江温州 325035
² 塞维利亚大学数学系塞维利亚 41012, 西班牙

收稿日期:2020-02-26 出版日期:2021-04-26 发布日期:2021-04-29
通讯作者: 赵才地 E-mail:xumingyue19@foxmail.com;zhaocaidi2013@163.com;caraball@us.es
作者简介:徐明月, E-mail: xumingyue19@foxmail.com|Tomás Caraballo, E-mail: caraball@us.es
基金资助:
国家自然科学基金(11971356);浙江省自然科学基金(LY17A010011)

Degenerate Regularity of Trajectory Statistical Solutions for the 3D Incompressible Navier-Stokes Equations

Mingyue Xu¹(),Caidi Zhao^1,*(),Caraballo Tomás²()

¹ Department of Mathematics, Wenzhou University, Zhejiang Wenzhou 325035
² Facultad de Mathmáticas, Universidad de Sevilla, Departmento de Ecuaciones Diferenciales y Análisis Numérico, 41012-Sevilla, Spain

Received:2020-02-26 Online:2021-04-26 Published:2021-04-29
Contact: Caidi Zhao E-mail:xumingyue19@foxmail.com;zhaocaidi2013@163.com;caraball@us.es
Supported by:
the NSFC(11971356);the NSF of Zhejiang Province(LY17A010011)

摘要/Abstract

摘要：

该文研究三维自治不可压Navier-Stokes方程组轨道统计解的退化正则性.作者证明了当该方程组的外力项具有$H^{-1}$正则性且Grashof数小于2.057时它的弱轨道统计解退化成具有部分正则性的统计解.同时也证明了当外力项具有$L^{2}$正则性且Grashof数小于2.057时它的轨道统计解退化成强轨道统计解.

关键词: 轨道统计解, 退化正则性, 三维不可压Navier-Stokes方程组, 轨道吸引子, Grashof数

Abstract:

In this article, the authors prove that if the (generalized) 3D Grashof number of the 3D autonomous incompressible Navier-Stokes equations is less than 2.057, then its weak trajectory statistical solutions possess (partial) degenerate regularity in the sense that they are supported by a set in which the weak solutions are in fact (partially) strong solutions. Also, they reveal that if the 3D Grashof number is less than 2.057, then the 3D incompressible Navier-Stokes equations possess only one complete and bounded strong solution which not only forward attracts but also pullback attracts its trajectories.

Key words: Trajectory statistical solution, Degenerate regularity, 3D incompressible Navier-Stokes equations, Trajectory attractor, Grashof number

中图分类号:

O.175.8

徐明月,赵才地,TomásCaraballo. 三维不可压Navier-Stokes方程组轨道统计解的退化正则性[J]. 数学物理学报, 2021, 41(2): 336-344.

Mingyue Xu,Caidi Zhao,Caraballo Tomás. Degenerate Regularity of Trajectory Statistical Solutions for the 3D Incompressible Navier-Stokes Equations[J]. Acta mathematica scientia,Series A, 2021, 41(2): 336-344.

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