  We present an isothermal fluctuating nonlinear hydrodynamic theory of
crystallization in molecular liquids. A dynamic coarse-graining technique is
used to derive the velocity field, a phenomenology, which allows a direct
coupling between the free energy functional of the classical Density Functional
Theory and the Navier-Stokes equation. Contrary to the Ginzburg-Landau type
amplitude theories, the dynamic response to elastic deformations is described
by parameter-free kinetic equations. Employing our approach to the free energy
functional of the Phase-Field Crystal model, we recover the classical spectrum
for the phonons and the steady-state growth fronts. The capillary wave spectrum
of the equilibrium crystal-liquid interface is in a good qualitative agreement
with the molecular dynamics simulations.

Materials Science;Soft Condensed Matter