On the low Mach number limit for Quantum Navier-Stokes equations
arXiv:1902.00402 · doi:10.1137/19M1252958
Abstract
We investigate the low Mach number limit for the 3-D quantum Navier-Stokes system. For general ill-prepared initial data, we prove strong convergence of finite energy weak solutions to weak solutions of the incompressible Navier-Stokes equations. Our approach relies on a quite accurate dispersive analysis for the acoustic part, governed by the well-known Bogoliubov dispersion relation for the elementary excitations of the weakly-interacting Bose gas. Once we have a control of the acoustic dispersion, the a priori bounds provided by the energy and Bresch-Desjardins entropy type estimates lead to the strong convergence. Moreover, for well-prepared data we show that the limit is a Leray weak solution, namely it satisfies the energy inequality. Solutions under consideration in this paper are not smooth enough to allow for the use of relative entropy techniques.
arXiv commentAuthor Accepted Manuscript (AAM)
References in corpus (11)
- On the Finite Energy Weak Solutions to a System in Quantum Fluid Dynamics
- Decay estimates for a class of wave equations
- The Quantum Hydrodynamics system in two space dimensions
- Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities
- Global Existence of Finite Energy Weak Solutions of Quantum Navier-Stokes Equations
- Global dispersive solutions for the Gross-Pitaevskii equation in two and three dimensions
- Energy equalities for compressible Navier-Stokes equations
- Scattering for the 3D Gross-Pitaevskii equation
- Quasineutral limit, dispersion and oscillations for Korteweg type fluids
- On the compactness of weak solutions to the Navier-Stokes-Korteweg equations for capillary fluids
- Global existence of finite energy weak solutions to the Quantum Navier-Stokes equations with non-trivial far-field behavior