Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (3): 629-641.

Previous Articles     Next Articles

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;;
  • 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)


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

CLC Number: 

  • O175.2