一维可压缩Navier-Stokes-Korteweg方程组的大初值整体光滑解（英文）  

GLOBAL SMOOTH SOLUTIONS TO THE 1-D COMPRESSIBLE NAVIER-STOKES-KORTEWEG SYSTEM WITH LARGE INITIAL DATA

作　　者：陈婷婷[1] 陈志春[1] 陈正争[1] CHEN Ting-ting CHEN Zhi-chun CHEN Zheng-zheng(School of Mathematical Sciences, Anhui University, Hefei 230601, China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《数学杂志》2017年第1期91-106,共16页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11426031);Undergraduate Scientific Research Training Program of Anhui University(ZLTS2015141)

摘　　要：本文研究了当粘性系数和毛细系数是密度函数的一般光滑函数时,一维等温的可压缩Navier-Stokes-Korteweg方程的Cauchy问题.利用基本能量方法和Kanel的技巧,得到了大初值、非真空光滑解的整体存在性与时间渐近行为.本文结果推广了已有文献中的结论.This paper is concerned with the Cauchy problem of the one-dimensional isothermal compressible Navier-Stokes-Korteweg system when the viscosity coefficient and capillarity coefficient are general smooth functions of the density. By using the elementary energy method and Kanel＇s technique [25], we obtain the global existence and time-asymptotic behavior of smooth non-vacuum solutions with large initial data, which improves the previous ones in the literature.

关 键 词：可压缩Navier-Stokes-Korteweg方程 整体存在性 时间渐近行为 大初值 

分 类 号：O175.29[理学—数学]