  We study hydrodynamic phonon heat transport in two-dimensional (2D)
materials. Starting from the Peierls-Boltzmann equation within the Callaway
model, we derive a 2D Guyer-Krumhansl-like equation describing non-local
hydrodynamic phonon transport, taking into account the quadratic dispersion of
flexural phonons. In additional to Poiseuille flow, second sound propagation,
the equation predicts heat current vortices and negative nonlocal thermal
conductance in 2D materials, common in classical fluid but scarcely considered
in phonon transport. Our results also illustrate the universal transport
behavior of hydrodynamics, independent on the type of quasi-particles and their
microscopic interactions.
