Lifshitz hydrodynamics at generic z from a moving black brane

A Lifshitz black brane at generic dynamical critical exponent $z > 1$, with non-zero linear momentum along the boundary, provides a holographic dual description of non-equilibrium steady state in quantum fluid, scale invariance but without boost symmetry. We consider moving branes Einstein-Maxwell-Dilaton gravity and obtain non-relativistic stress tensor complex field theory via suitable renormalisation procedure. The resulting hydrodynamics thermodynamics are concrete realization perfect fluid exponent.