We establish a well-posedness result for the hydrodynamical form (HGP) of the one dimensional Gross-Pitaevskii equation (GP) via the classical form of this equation. The result established in this way proves that (HGP) is locally well-posed since the solution of (GP) can be vanished at some $t\neq 0.$
Hydrodynamical form for the one-dimensional Gross-Pitaevskii equation