  We study theoretically the non-equilibrium exciton transport in monolayer
transition metal dichalcogenides. We consider the situation where excitons
interact with non-equilibrium phonons, e.g., under the conditions of localized
excitation where a ``hot spot'' in formed. We develop the theory of the exciton
drag by the phonons and analyze in detail the regimes of diffusive propagation
of phonons and ballistic propagation of phonons where the phonon wind is
formed. We demonstrate that a halo-like spatial distribution of excitons akin
observed in [Phys. Rev. Lett. 120, 207401 (2018)] can be formed as a result of
the exciton drag by non-equilibrium phonons or Seebeck effect.
