  We analyze continuous data assimilation by nudging for the 3D Ladyzhenskaya
equations. The analysis provides conditions on the spatial resolution of the
observed data that guarantee synchronization to the reference solution
associated with the observed, spatially coarse data. This synchronization holds
even though it is not known whether the reference solution, with initial data
in $L^2$, is unique; a particular reference solution is determined by the
observed, coarse data. The efficacy of the algorithm in both 2D and 3D is
demonstrated by numerical computations.
