Global Existence of Finite Energy Weak Solutions of Quantum Navier-Stokes Equations

Abstract

In this paper we consider the Quantum Navier-Stokes system both in two and in three space dimensions and prove global existence of finite energy weak solutions for large initial data. In particular, the notion of weak solutions is the standard one. This means that the vacuum region are included in the weak formulations. In particular, no extra term like damping or cold pressure are added to the system in order to define the velocity field in the vacuum region. The main contribution of this paper is the construction of a regular approximating system consistent with the effective velocity transformation needed to get necessary a priori estimates.

Updated to Author Accepted Manuscript

References in corpus (2)

• On the Finite Energy Weak Solutions to a System in Quantum Fluid Dynamics
• Global well-posedness of the Euler-Korteweg system for small irrotational data

Cited by in corpus (7)

• On the compactness of weak solutions to the Navier-Stokes-Korteweg equations for capillary fluids
• On the low Mach number limit for Quantum Navier-Stokes equations
• Relaxation limit from the Quantum-Navier-Stokes equations to the Quantum Drift Diffusion equation
• Global existence of finite energy weak solutions to the Quantum Navier-Stokes equations with non-trivial far-field behavior
• Global existence of weak solutions to the compressible quantum Navier-Stokes equations with degenerate viscosity
• On the mass transfer in the 3D Pitaevskii model
• Small-data global existence of solutions for the Pitaevskii model of superfluidity