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We simulate by lattice Boltzmann the steady shearing of a binary fluid mixture undergoing phase separation with full hydrodynamics in two dimensions. Contrary to some theoretical scenarios, a dynamical steady state is attained with finite domain lengths L-x,L-y in the directions (x,y) of velocity and velocity gradient. Apparent scaling exponents are estimated as L-x similar to gamma(-2/3) and L-y similar to gamma(-3/4). We discuss the relative roles of diffusivity and hydrodynamics in attaining steady state.