  This paper studies the one dimensional Navier-Stokes-Fourier-Korteweg system
of equations describing the evolution of a heat-conducting compressible fluid
that exhibits viscosity and capillarity. The main goal of the present analysis
is to examine the dissipative structure of the system and to prove the global
existence and the asymptotic decay of perturbations of equilibrium states. For
that purpose, a novel nonlinear change of perturbed state variables, which
takes into account that the conserved quantities contain density gradients, is
introduced. These new perturbation variables satisfy a partially symmetric
system whose linearization fulfills the generalized genuine coupling condition
of Humpherys (J. Hyperbolic Differ. Equ. 2, 2005, no. 4, 963-974) for higher
order systems. It is shown that the linearized system is symbol symmetrizable
and an appropriate compensating matrix is constructed. This procedure allows to
obtain linear decay rates which underlie a dissipative mechanism of
regularity-gain type. This linear dissipative structure implies, in turn, the
global decay of small perturbations to constant equilibrium states as solutions
to the full nonlinear system.
