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We construct the general first-order hydrodynamic theory invariant under timetranslations, the Euclidean group of spatial transformations and preservingparticle number, that is with symmetry group$\mathbb{R}_t\times$ISO$(d)\times$U$(1)$. Such theories are important in anumber of distinct situations, ranging from the hydrodynamics of graphene toflocking behaviour and the coarse-grained motion of self-propelled organisms.Furthermore, given the generality of this construction, we are are able todeduce special cases with higher symmetry by taking the appropriate limits. Inthis way we write the complete first-order theory of Lifshitz-invarianthydrodynamics. Among other results we present a class of non-dissipative firstorder theories which preserve parity.

Hydrodynamics without boosts