Global weak solutions to compressible quantum Navier-Stokes equations with damping
Abstract
The global-in-time existence of weak solutions to the barotropic compressible quantum Navier-Stokes equations with damping is proved for large data in three dimensional space. The model consists of the compressible Navier-Stokes equations with degenerate viscosity, and a nonlinear third-order differential operator, with the quantum Bohm potential, and the damping terms. The global weak solutions to such system is shown by using the Faedo-Galerkin method and the compactness argument. This system is also a very important approximated system to the compressible Navier-Stokes equations. It will help us to prove the existence of global weak solutions to the compressible Navier-Stokes equations with degenerate viscosity in three dimensional space.
Keywords
Cite
@article{arxiv.1503.06894,
title = {Global weak solutions to compressible quantum Navier-Stokes equations with damping},
author = {Alexis F. Vasseur and Cheng Yu},
journal= {arXiv preprint arXiv:1503.06894},
year = {2015}
}
Comments
This paper provides the existence of the approximation in arXiv:1501.06803