On consistency of hydrodynamic approximation for chiral media

We consider chiral liquids, that is liquids consisting of massless fermions and right-left asymmetric. In such media, one expects existence of electromagnetic current flowing along an external magnetic field, associated with the chiral anomaly. The current is predicted to be dissipation-free. We consider dynamics of chiral liquids, concentrating on the issues of possible instabilities and infrared sensitivity. Instabilities arise, generally speaking, already in the limit of vanishing electromagnetic constant, $\alpha_{el}\to 0$. In particular, liquids with non-vanishing chiral chemical potential might decay into right-left asymmetric states containing vortices.