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In this note, we investigate linear instabilities of hydrodynamics withcorrections up to first order in derivatives. It has long been known thatrelativistic (Lorentzian) first order hydrodynamics, with positive localentropy production, exhibits unphysical instabilities. We extend this analysisto fluids with Galilean and Carrollian boost symmetries. We find that theinstabilities occur in all cases, except for fluids with Galilean boostsymmetry combined with the choice of macroscopic variables called Eckart frame.We also present a complete linearised analysis of the full spectrum of firstorder Carrollian hydrodynamics. Furthermore, we show that even in a fluidwithout boost symmetry present, instabilities can occur. These results provideevidence that the unphysical instabilities are symptoms of first orderhydrodynamics, rather than a special feature of Lorentzian fluids.

First order non-Lorentzian fluids, entropy production and linear instabilities