Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 48, Issue 2, Pages 1489-1511Publisher
SIAM PUBLICATIONS
DOI: 10.1137/15M1013730
Keywords
global weak solutions; compressible quantum Navier-Stokes equations; approximated system; vacuum; degenerate viscosity
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Funding
- NSF [DMS-1209420]
- AMS-Simons Travel Grant
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In this paper, we proved the existence of global weak solutions of the compressible quantum Navier-Stokes equations with large data in three dimensions (3D). The model consists of the compressible Navier-Stokes equations with degenerate viscosity, a nonlinear third-order differential operator known as the quantum Bohm potential, and some damping terms. The global weak solution is shown by using the Faedo-Galerkin method and the compactness arguments. This system is also an approximation 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 3D.
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