  We present the nonlinear fluctuating hydrodynamics which governs the late
time dynamics of a chaotic many-body system with simultaneous charge/mass,
dipole/center of mass, and momentum conservation. This hydrodynamic effective
theory is unstable below four spatial dimensions: dipole-conserving fluids at
rest become unstable to fluctuations, and are governed not by hydrodynamics,
but by a fractonic generalization of the Kardar-Parisi-Zhang universality
class. We numerically simulate many-body classical dynamics in one-dimensional
models with dipole and momentum conservation, and find evidence for a breakdown
of hydrodynamics, along with a new universality class of undriven yet
non-equilbrium dynamics.
