数学季刊 >

2016 , Vol. 31 >Issue 1: 27 - 38

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2016.01.004

一维 Navier-Stokes-Korteweg 方程整体解的存在性唯一性和指数稳定性

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  • 1. College of Information Science and Technology, Donghua University2. Department of Applied Mathematics, Zhongyuan University of Technology
ZHANG Jian-lin(1977-), male, native of Luoyang, Henan, an associate professor of Zhongyuan University of Technology and a Ph.D. candidate of Donghua University, engages in nonlinear evolution equations and infinite-dimensional dynamical systems.

收稿日期: 2015-12-20

  网络出版日期: 2020-11-12

基金资助

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

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

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  • 1. College of Information Science and Technology, Donghua University2. Department of Applied Mathematics, Zhongyuan University of Technology
ZHANG Jian-lin(1977-), male, native of Luoyang, Henan, an associate professor of Zhongyuan University of Technology and a Ph.D. candidate of Donghua University, engages in nonlinear evolution equations and infinite-dimensional dynamical systems.

Received date: 2015-12-20

  Online published: 2020-11-12

Supported by

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

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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 H2×H1× H1 for the one-dimensional Navier-Stokes-Korteweg equations by a priori estimates,which implies the existence and exponential stability of the nonlinear C0-semigroups S（t） on H2× H1× H1. 

关键词： Navier-Stokes equations; capillarity; Korteweg stress tensor

本文引用格式

张建林, 曹洁, 苏兴 . 一维 Navier-Stokes-Korteweg 方程整体解的存在性唯一性和指数稳定性[J]. 数学季刊, 2016 , 31(1) : 27 -38 . DOI: 10.13371/j.cnki.chin.q.j.m.2016.01.004

Abstract

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 H2×H1× H1 for the one-dimensional Navier-Stokes-Korteweg equations by a priori estimates,which implies the existence and exponential stability of the nonlinear C0-semigroups S（t） on H2× H1× H1. 

Key words： Navier-Stokes equations; capillarity; Korteweg stress tensor

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