Global existence of weak solutions to the Navier-Stokes-Korteweg equations

P. Antonelli, L. Hientzsch and P. Marcati. On the Low Mach number limit for Quantum-Navier-Stokes equations

Original

1902

Earlier work this paper cites.

J.E. Dunn and J. Serrin, On the thermomechanics of interstitial working , Arch. Ration. Mech. Anal., 88

1985

Earlier work this paper cites.

R. J. DiPerna and P. L. Lions,

1989

Earlier work this paper cites.

L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions

1992

Earlier work this paper cites.

H. Hattori and D. Li, Solutions for two dimensional system for materials of Korteweg type

1994

Earlier work this paper cites.

H. Hattori and D. Li, Global solutions of a high dimensional system for Korteweg materials

1996

Earlier work this paper cites.

P.L. Lions, Mathematical Topics in Fluid Mechanics. Vol. 2

1996

Earlier work this paper cites.

E. Feireisl, On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable

2001

Earlier work this paper cites.

D. Bresch and D. Desjardins, Sur un modèle de Saint-Venant visqueux et sa limite quasi-géostrophique. [On viscous shallow-water equations (Saint-Venant model) and the quasi-geostrophic limit.]

2002

Earlier work this paper cites.

D. Bresch, B. Desjardins and Chi-Kun Lin, On some compressible fluid models: Korteweg, lubrication, and shallow water systems

2003

Earlier work this paper cites.

S. Benzoni-Gavage, R. Danchin and S. Descombes, On the well-posedness for the Euler-Korteweg model in several space dimensions , Indiana Univ. Math. J., 56

2007

Cited alongside, same era.

A. Mellet and A. Vasseur, On the barotropic compressible Navier-Stokes equations

2007

Cited alongside, same era.

P. Antonelli and P. Marcati, On the finite energy weak solutions to a system in quantum fluid dynamics,

2009

Cited alongside, same era.

A. Jüngel, Global weak solutions to compressible Navier-Stokes equations for quantum fluids

2010

Cited alongside, same era.

P. Antonelli and P. Marcati, The Quantum Hydrodynamics system in two space dimensions , Arch. Ration. Mech. Anal., 203

2012

Cited alongside, same era.

D. Bresch, F. Couderc, P. Noble, J.P. Vila, A generalization of the quantum Bohm identity: Hyperbolic CFL condition for the Euler-Korteweg equations, Généralisation de l’identité de Bohm quantique : condition CFL hyperbolique pour équations d’Euler–Korteweg. , Comptes Rendus Math. 354

2016

Later among the works it cites.

D. Donatelli and P. Marcati, Low Mach number limit for the quantum hydrodynamics system

2016

Later among the works it cites.

A. Vasseur and C. Yu, Global weak solutions to compressible quantum Navier-Stokes equations with damping

2016

Later among the works it cites.

P. Antonelli and S. Spirito, Global existence of finite energy weak solutions of quantum Navier-Stokes equations , Arch. Ration. Mech. Anal., 3

2017

Later among the works it cites.

C. Audiard and B. Haspot, Global well-posedness of the Euler-Korteweg system for small irrotational data