  In this note, we investigate linear instabilities of hydrodynamics with
corrections up to first order in derivatives. It has long been known that
relativistic (Lorentzian) first order hydrodynamics, with positive local
entropy production, exhibits unphysical instabilities. We extend this analysis
to fluids with Galilean and Carrollian boost symmetries. We find that the
instabilities occur in all cases, except for fluids with Galilean boost
symmetry combined with the choice of macroscopic variables called Eckart frame.
We also present a complete linearised analysis of the full spectrum of first
order Carrollian hydrodynamics. Furthermore, we show that even in a fluid
without boost symmetry present, instabilities can occur. These results provide
evidence that the unphysical instabilities are symptoms of first order
hydrodynamics, rather than a special feature of Lorentzian fluids.

High Energy Physics - Theory;General Relativity and Quantum Cosmology;Fluid Dynamics