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

• 论文 • 上一篇    下一篇

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. 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 Li2,3(),Xing Wu4,*()   

  1. 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:

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