On the Low Mach Number Limit for Quantum Navier--Stokes Equations

Low Mach number limit of the full Navier-Stokes equations,

The low Mach number limit for classical solutions of the full Navier-Stokes equations is here studied. The combined effects of large temperature variations and thermal conduction are taken into account. In particular, we consider general initial data. The equations lead to a singular problem whose linearized is not uniformly well-posed. Yet, it is proved that the solutions exist and are uniform...

Adjoint algorithms for the Navier-Stokes equations in the low Mach number limit

This paper describes a derivation of the adjoint low Mach number equations and their implementation and validation within a global mode solver. The advantage of using the low Mach number equations and their adjoints is that they are appropriate for flows with variable density, such as flames, but do not require resolution of acoustic waves. Two versions of the adjoint are implemented and assess...

A Low Mach Number Limit of a Dispersive Navier-Stokes System

We establish a low Mach number limit for classical solutions over the whole space of a compressible fluid dynamic system that includes dispersive corrections to the Navier-Stokes equations. The limiting system is a ghost effect system [26]. Our analysis builds upon the framework developed by Métivier and Schochet [20] and Alazard [2] for non-dispersive systems. The strategy involves establishin...

Nečas Center for Mathematical Modeling Low Mach number limit for the Navier-Stokes system on unbounded domains under strong stratification

Quantum Navier–Stokes equations

Compressible Navier–Stokes models for quantum fluids are reviewed. They are derived from a collisional Wigner equation by a moment method and a Chapman–Enskog expansion around the quantum equilibrium. Introducing a new velocity variable, the barotropic quantum Navier-Stokes model can be reformulated as a viscous quantum Euler system, which possesses a new Lyapunov (energy) functional. This func...