Global weak solutions for quantum isothermal fluids

We construct global weak solutions to isothermal quantum Navier–Stokes equations, with or without Korteweg term, in the whole space of dimension at most three. Instead working on initial set unknown functions, we consider an equivalent reformulation, based a time-dependent rescaling, that introduced previous paper study large time behavior, and which provides suitable priori estimates, as opposed formulation where potential energy is not signed. proceed by tori whose size eventually becomes infinite. On each fixed torus, equations presence drag force terms. Such are solved regularization, limit terms vanish treated resuming notion renormalized solution developed I. Lacroix-Violet A. Vasseur. also establish existence for equation (no viscosity), when data well-prepared, sense they stem from Madelung transform.