Asymptotic limit of a Navier-Stokes-Korteweg system with density-dependent viscosity

Jianwei Yang; Peng Cheng; Yudong Wang

doi:10.3934/era.2015.22.20

Article Contents

2015, Volume 22: 20-31. Doi: 10.3934/era.2015.22.20 open access

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Asymptotic limit of a Navier-Stokes-Korteweg system with density-dependent viscosity

1.
College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450045, Henan Province

Received: April 30, 2014

Revised: January 31, 2015

Published: December 2014

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Abstract

In this paper, we study a combined incompressible and vanishing capillarity limit in the barotropic compressible Navier-Stokes-Korteweg equations for weak solutions. For well prepared initial data, the convergence of solutions of the compressible Navier-Stokes-Korteweg equations to the solutions of the incompressible Navier-Stokes equation are justified rigorously by adapting the modulated energy method. Furthermore, the corresponding convergence rates are also obtained.

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Mathematics Subject Classification: 35Q30, 35B40, 35C20.

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