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

ZHANG Jian-lin, CAO Jie, SU Xing

doi:10.13371/j.cnki.chin.q.j.m.2016.01.004

Chinese Quarterly Journal of Mathematics >

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

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

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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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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ZHANG Jian-lin, CAO Jie, SU Xing . A Remark on Global Existence, Uniqueness and Exponential Stability of Solutions for the 1D Navier-Stokes-Korteweg Equations[J]. Chinese Quarterly Journal of Mathematics, 2016 , 31(1) : 27 -38 . DOI: 10.13371/j.cnki.chin.q.j.m.2016.01.004

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