Communications in Mathematical Sciences
Volume 12 (2014)
Decay estimates of the non-isentropic compressible fluid models of Korteweg type in $R^3$
Pages: 1437 – 1456
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.