Dynamics of Fluids without Boost Symmetries

Standard textbook treatments of fluid dynamics assume the presence of a boost symmetry. This is either a Galilean boost symmetry or a Lorentzian one and leads to the Navier-Stokes equations or their relativistic counterpart. It is however not necessary to rely on a boost symmetry as one can treat velocity as the chemical potential associated with momentum conservation. In fact for fluids moving through a medium one expects boost symmetries to be generically broken. This includes the case of scale invariant Lifshitz fluids. In this talk I will present the general treatment of fluid dynamics without boost symmetries and I will show that there can be 10 dissipative and 6 non-dissipative transport coefficients (of which 2 are hydrostatic and 4 are not) for uncharged non-boost invariant fluid dynamics. I will end with some comments regarding holographic realisations of non-boost invariant Lifshitz fluids.