Asymptotic behavior of Navier-Stokes-Korteweg with friction in $\mathbb{R}^{3}$

Zhong Tan; Xu Zhang; Huaqiao Wang

doi:10.3934/dcds.2014.34.2243

Article Contents

2014, Volume 34, Issue 5: 2243-2259. Doi: 10.3934/dcds.2014.34.2243

This issue Previous Article Symbolic dynamics for the geodesic flow on two-dimensional hyperbolic good orbifolds Next Article Scattering theory for the wave equation of a Hartree type in three space dimensions

Asymptotic behavior of Navier-Stokes-Korteweg with friction in $\mathbb{R}^{3}$

1.
School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005
2.
School of Mathematical Sciences, Xiamen University, Fujian 361005

Received: March 2013

Revised: July 2013

Published: May 2014

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Abstract

We consider the compressible barotropic Navier-Stokes-Korteweg system with friction in this paper. The global solutions and optimal convergence rates are obtained by pure energy method provided the initial perturbation around a constant state is small enough. In particular, the decay rates of the higher-order spatial derivatives of the solution are obtained. Our proof is based on a family of scaled energy estimates and interpolations among them without linear decay analysis.

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Mathematics Subject Classification: Primary: 35Q30, 76N10; Secondary: 76D05.

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