  We present a theory of thermoelectric transport in weakly disordered Weyl
semimetals where the electron-electron scattering time is faster than the
electron-impurity scattering time. Our hydrodynamic theory consists of
relativistic fluids at each Weyl node, coupled together by perturbatively small
inter-valley scattering, and long-range Coulomb interactions. The conductivity
matrix of our theory is Onsager reciprocal and positive-semidefinite. In
addition to the usual axial anomaly, we account for the effects of a distinct,
axial-gravitational anomaly expected to be present in Weyl semimetals. Negative
thermal magnetoresistance is a sharp, experimentally accessible signature of
this axial-gravitational anomaly, even beyond the hydrodynamic limit.
