Summary: When fluid in a rectangular tank sits upon a platform which is oscillating with sufficient amplitude, surface waves appear in the ``Faraday resonance.'' Scientists and engineers have done bifurcation analyses which assume that there is a center manifold theorem for Xiao-Biao Lin's model in which potential flow is assumed, but an artificial dissipation term is included in the system of partial differential equations on the free surface. We use interpolation spaces, establish maximal regularity for a family of evolution operators, and adapt the center manifold theory.