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 oppos...

Evolution equations which describe the changes in a velocity field over time have been classically studied within Eulerian or Lagrangian frame of reference. Classically, these frameworks are equivalent descriptions same problem, and equivalence can be demonstrated by constructing particle paths. For hyperbolic conservation laws, we extend between to weak solutions for broad class problems. Our ...