The equations of phonon hydrodynamics are re-considered in the framework of expansions of the phonon kinetic equation for large frequency of momentum conserving N-processes. Specifically, the Chapman-Enskog expansion provides a sound derivation of non-linear transport equations that fulfill all necessary compatibility requirements. The celebrated Guyer-Krumhansl equations can only be derived under the more restrictive condition of slow processes, and are affected by compatibility problems. The impact of different energy-temperature relations on the structure of equations is discussed.