Uniqueness of weak solutions to a non-linear hyperbolic system in electrohydrodynamics

In this note we prove the uniqueness of weak solutions to a nonlinear hyperbolic system in electrohydrodynamics without the effects of a dissociation-recombination process. It is still open in the presence of a special dissociation-recombination process, although the existence of at least one weak solution was proved via the method of renormalized solutions by Feireisl [E. Feireisl, Weak solutions to a non-linear hyperbolic system arising in the theory of dielectric liquids, Math. Methods Appl. Sci. 18 (1995) 1041-1052] in 1995.