  One proves here the backward uniqueness of solutions to stochastic semilinear
parabolic equations and also for the tamed Navier-Stokes equations driven by
linearly multiplicative Gaussian noises. Applications to approximate
controllability of nonlinear stochastic parabolic equations with initial
controllers are given. The method of proof relies on the logarithmic convexity
property known to hold for solutions to linear evolution equations in Hilbert
spaces with self-adjoint principal part.
