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arXiv · 1503.06894

Global weak solutions to compressible quantum Navier-Stokes equations with damping

Alexis F. Vasseur·Cheng Yu
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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.

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Alexis F. Vasseur, Cheng Yu. 2015-03-24. Global weak solutions to compressible quantum Navier-Stokes equations with damping. https://arxiv.org/abs/1503.06894

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