A Remark on Global Existence,Uniqueness and Exponential Stability of Solutions for the 1D Navier-Stokes-Korteweg Equations  

作　　者：ZHANG Jian-lin CAO Jie SU Xing 

机构地区：[1]College of Information Science and Technology,Donghua University,Shanghai 201620,China [2]Department of Applied Mathematics,Zhongyuan University of Technology,Zhengzhou 450007,China

出　　处：《Chinese Quarterly Journal of Mathematics》2016年第1期27-38,共12页数学季刊（英文版）

基　　金：Supported by the National Natural Science Foundation of China(11271066);Supported by the Shanghai Education Commission(13ZZ048)

摘　　要：In this paper, we investigate non-isothermal one-dimensional model of capillary compressible fluids as derived by M Slemrod(1984) and J E Dunn and J Serrin(1985). We establish the existence, uniqueness and exponential stability of global solutions in H^2×H^1× H^1 for the one-dimensional Navier-Stokes-Korteweg equations by a priori estimates,which implies the existence and exponential stability of the nonlinear C_0-semigroups S(t) on H^2× H^1× H^1.In this paper, we investigate non-isothermal one-dimensional model of capillary compressible fluids as derived by M Slemrod（1984） and J E Dunn and J Serrin（1985）. We establish the existence, uniqueness and exponential stability of global solutions in H^2×H^1× H^1 for the one-dimensional Navier-Stokes-Korteweg equations by a priori estimates,which implies the existence and exponential stability of the nonlinear C_0-semigroups S（t） on H^2× H^1× H^1.

关 键 词：Navier-Stokes equations CAPILLARITY Korteweg stress tensor 

分 类 号：O175.29[理学—数学]