Exact integrability conditions for cotangent vector fields

Stefano Bianchini

In Quantum Hydro-Dynamics the following problem is relevant: let $(\sqrt{\rho },\Lambda )\in H^1({\mathbb{R}}^d)\times L^2({\mathbb{R}}^d,{\mathbb{R}}^d)$ be a finite energy hydrodynamics state, i.e. $\Lambda =0$ when $\rho =0$ an…