Communications in Mathematical Sciences

Volume 12 (2014)

Number 8

Decay estimates of the non-isentropic compressible fluid models of Korteweg type in $R^3$

Pages: 1437 – 1456



Xu Zhang (School of Mathematical Sciences, Xiamen University, Fujian, China)

Zhong Tan (School of Mathematical Sciences, Xiamen University, Fujian, China)


The existence and optimal convergence rates of global-in-time classical solutions to the Cauchy problem for the compressible non-isotropic Navier-Stokes-Korteweg system for small initial perturbation is obtained. The global solution is obtained by combining the local existence and the a priori estimates provided the initial perturbation around a constant state is small enough. The optimal convergence rates are obtained by energy estimates and interpolation inequalities, and without linear decay analysis.


Navier-Stokes equations, Korteweg, optimal decay rates, energy method, Sobolev interpolation

2010 Mathematics Subject Classification

Primary 35Q30, 76N10. Secondary 76D05.

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