三维Navier-Stokes-Korteweg方程组的整体大解

数学物理学报 ›› 2021, Vol. 41 ›› Issue (3): 629-641.

三维Navier-Stokes-Korteweg方程组的整体大解

于洋海¹(),李金禄^2,³(),吴星^4,*()

¹ 安徽师范大学数学与统计学院安徽芜湖 241002
² 广州大学数学与信息科学学院广州 510006
³ 赣南师范大学数学与计算机科学学院江西赣州 341000
⁴ 河南农业大学信息与管理科学学院郑州 450002

收稿日期:2020-06-11 出版日期:2021-06-26 发布日期:2021-06-09
通讯作者: 吴星 E-mail:yuyanghai214@sina.com;lijinlu@gnnu.cn;ny2008wx@163.com
作者简介:于洋海, E-mail: yuyanghai214@sina.com|李金禄, E-mail: lijinlu@gnnu.cn
基金资助:
安徽省自然科学基金(1908085QA05);安徽师范大学博士科研启动基金;国家自然科学基金(11801090);中国博士后科学基金(2020T130129);中国博士后科学基金(2020M672565)

A Class of Global Large Solutions to 3D Navier-Stokes-Korteweg Equations

Yanghai Yu¹(),Jinlu Li^2,³(),Xing Wu^4,*()

¹ School of Mathematics and Statistics, Anhui Normal University, Anhui Wuhu 241002
² School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006
³ School of Mathematics and Computer Sciences, Gannan Normal University, Jiangxi Ganzhou 341000
⁴ College of Information and Management Science, Henan Agricultural University, Zhengzhou 450002

Received:2020-06-11 Online:2021-06-26 Published:2021-06-09
Contact: Xing Wu E-mail:yuyanghai214@sina.com;lijinlu@gnnu.cn;ny2008wx@163.com
Supported by:
the NSF of Anhui Province(1908085QA05);the PhD Scientific Research Start-up Foundation of Anhui Normal University;the NSFC(11801090);the Postdoctoral Science Foundation of China(2020T130129);the Postdoctoral Science Foundation of China(2020M672565)

摘要/Abstract

摘要：

该文研究$\mathbb{R}^3$上的可压缩Navier-Stokes-Korteweg方程组的Cauchy问题.通过选取特殊的Korteweg张量，证明了该方程组在某类大初值下存在整体解.这里的“大”是指初始速度和初始涡度的第三分量的$L^{\infty}$范数都可以任意大.

关键词: Navier-Stokes-Korteweg方程组, 整体大解

Abstract:

In this paper, we consider the Cauchy problem to the tri-dimensional compressible Navier-Stokes-Korteweg system with a specific choice on the Korteweg tensor in $\mathbb{R}^3$, and construct the global solutions to the tri-dimensional Navier-Stokes-Korteweg equations with a class of of large initial data, where the $L^{\infty}$ norm of the initial velocity and the third component of initial vorticity could be arbitrarily large.

Key words: Navier-Stokes-Korteweg, Large solutions

中图分类号:

O175.2

于洋海,李金禄,吴星. 三维Navier-Stokes-Korteweg方程组的整体大解[J]. 数学物理学报, 2021, 41(3): 629-641.

Yanghai Yu,Jinlu Li,Xing Wu. A Class of Global Large Solutions to 3D Navier-Stokes-Korteweg Equations[J]. Acta mathematica scientia,Series A, 2021, 41(3): 629-641.

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