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This paper is dedicated to the construction of global weak solutions to the quantum Navier-Stokes equation, for any initial value with bounded energy and entropy.
Pressure and stress tensor expressions in the fluid mechanical formulation of the Bose condensate equations
J. Grant · 1973
Earlier work this paper cites.
Form of the quantum potential for use in hydrodynamic equations for semiconductor device modeling
D. Ferry and J.-R. Zhou · 1993
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On the creation of quantum vortex lines in rotating He II
M. Loffredo and L. Morato · 1993
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Mathematical topics in fluid mechanics. Vol. 1
P.-L. Lions · 1996
Earlier work this paper cites.
Existence of global weak solutions for 2D viscous shallow water equations and convergence to the quasi-geostrophic model
D. Bresch and B. Desjardins · 2003
Earlier work this paper cites.
On some compressible fluid models: Korteweg, lubrication and shallow water systems
D. Bresch, B. Desjardins, and C.K. Lin · 2003
Earlier work this paper cites.
Quantum Dynamics with Trajectories
R. Wyatt · 2005
Cited alongside, same era.
On the existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids
D. Bresch and B. Desjardins · 2007
Cited alongside, same era.
On the barotropic compressible Navier-Stokes equations
A. Mellet and A. Vasseur · 2007
Cited alongside, same era.
Derivation of viscous correction terms for the isothermal quantum Euler model
S. Brull and F. Méhats · 2010
Cited alongside, same era.
Global weak solutions to compressible Navier-Stokes equations for quantum fluids
A. Jüngel · 2010
Cited alongside, same era.
On the flow of chemically reacting gaseous mixture
E. Zatorska · 2012
Cited alongside, same era.
About the barotropic compressible quantum Navier-Stokes equations
M. Gisclon and I. Lacroix-Violet · 2015
Later among the works it cites.
J. Li and Zh. Xin · 2015
Later among the works it cites.
Existence of global weak solutions for 3d degenerate compressible navier-stokes equations
A. Vasseur and Ch. Yu · 2015
Later among the works it cites.
Global existence of finite energy weak solutions of quantum navier-stokes equations
P. Antonelli and S. Spirito · 2016
Closest in time.
Global Weak Solutions to the Compressible Quantum Navier–Stokes Equations with Damping
A. Vasseur and Ch. Yu · 2016
Closest in time.
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