  We present a new derivation for the optimal decay of \textit{arbitrary}
higher order derivatives for $L^p$ solutions to the compressible fluid model of
Korteweg type. This approach, based on Gevrey estimates, is to establish
uniform bounds on the growth of the radius of analyticity of the solution in
negative Besov norms. For that end, the maximal regularity property involving
Gevrey multiplier of heat kernel and non standard product Besov estimates are
well developed. Our approach is partly inspired by Oliver-Titi's work and is
applicable to a wide range of dissipative systems.
