The well-posedness of the Cauchy problem for self-interacting vector fields

We point out that the initial-value (Cauchy) problem for self-interacting vector fields presents same well-posedness issues as first-order derivative scalar (often referred to $k$-essence). For latter, suitable strategies have been employed in last few years successfully evolve Cauchy at level of infrared theory, without need an explicit ultraviolet completion. argue very techniques can also be applied fields, avoiding a number and "pathologies" recently found literature.