On Well-Posedness of Quantum Fluid Systems in the Class of Dissipative Solutions

Abstract

The main objects of the present work are the quantum Navier–Stokes and quantum Euler systems; for the first one, in particular, we will consider constant viscosity coefficients. We deal with the concept of dissipative solutions, for which we will first prove the weak-strong uniqueness principle, and afterward, we will show the global existence for any finite energy initial data. Finally, we will prove that both systems admit a semiflow selection in the class of dissipative solutions.