  I derive up to second order in Eulerian perturbation theory a new relation
between the weakly nonlinear density and velocity fields. In the case of
unsmoothed fields, density at a given point turns out to be a purely local
function of the expansion (divergence) and shear of the velocity field. The
relation depends on the cosmological parameter Omega, strongly by the factor
f(Omega) = Omega^{0.6} and weakly by the factors K(Omega) and C(Omega)
proportional to Omega^{-2/63} and Omega^{-1/21} respectively. The Gramann
solution is found to be equivalent to the derived relation with the weak
Omega-dependence neglected. To make the relation applicable to the real world,
I extend it for the case of smoothed fields. The resulting formula, when
averaged over shear given divergence, reproduces up to second order the
density-velocity divergence relation of Chodorowski & Lokas; however, it has
smaller spread. It makes the formula a new attractive local estimator of
large-scale density from velocity.
