Breakdown of conventional hydrodynamics in three-dimensional systems with long-ranged two-dimensional translational order

The influence of anharmonic elastic terms on the hydrodynamics of discotic liquid crystals is examined. These terms generate a nonlinear coupling between the velocity field and thermally excited undulation modes which, it is shown, causes four of the five viscosities in these systems to diverge as ${\omega }^{-\frac{1}{2}}$ at small frequencies $\omega$. This implies that the attenuation of sound in these systems should scale as ${\omega }^{\frac{3}{2}}$ (not ${\omega }^2$ as in conventional materials). A simple relation between three of the diverging viscosities is found. Various experimental tests of these predictions are suggested.