Fetching the paper…
Reading the bibliography…
In this paper we consider the Quantum Navier-Stokes system both in two and in three space dimensions and prove global existence of finite energy weak solutions for large initial data.
O. Ladyzhenskaya, V. A. Solonnikov, N. N. Uraltseva, Linear and quasilinear equations of parabolic type , Translated from the Russian by S. Smith. Translations of Mathematical Monographs, Vol. 23. American Mathematical Society, Providence, R.I., 1968
1968
Earlier work this paper cites.
L. Landau, E. Lifschitz, Quantum mechanics: non-relativistic theory , Pergamon Press, New York, 1977
1977
Earlier work this paper cites.
E.A. Carlen, Conservative diffusions , Comm. Math. Phys., 94, (1984), 293–315
1984
Earlier work this paper cites.
J.E. Dunn, J. Serrin, On the thermomechanics of interstitial working , Arch. Rat. Mech. Anal., 88, (1985), no. 2, 95–133
1985
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, B. 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, Chi-Kun Lin, On some compressible fluid models: Korteweg, lubrication, and shallow water systems
2003
Earlier work this paper cites.
D. Bresch, B. Desjardins, Some diffusive capillary models of Korteweg type , C. R. Math. Acad. Sci. Paris, 332 (2004), 881–886
2004
Earlier work this paper cites.
Z. Wu, J. Yin and C. Wang, Elliptic and parabolic equations
2006
Earlier work this paper cites.
S. Benzoni-Gavage, R. Danchin, S. Descombes, On the well-posedness for the Euler-Korteweg model in several space dimensions , Indiana Univ. Math. J., 56, (2007), 1499–1579
2007
Earlier work this paper cites.
A. Mellet, A. Vasseur, On the barotropic compressible Navier-Stokes equations
2007
Earlier work this paper cites.
P. Antonelli and P. Marcati. On the finite energy weak solutions to a system in quantum fluid dynamics
2009
Cited alongside, same era.
S. Brull and F. Méhats, Derivation of viscous correction terms for the isothermal quantum Euler model
2010
Cited alongside, same era.
A. Jüngel, Global weak solutions to compressible Navier-Stokes equations for quantum fluids
2010
Cited alongside, same era.
F. Jiang, A remark on weak solutions to the barotropic compressible quantum Navier-Stokes equations , Nonlin. Anal. RWA 12
2011
Cited alongside, same era.
A. Jüngel, Effective velocity in Navier-Stokes equations with third-order derivatives
2011
Cited alongside, same era.
P. Antonelli and P. Marcati, The Quantum Hydrodynamics system in two space dimensions , Arch. Rat. Mech. Anal., 203, (2012), 499–527
Z. Chen, X. Chai, B. Dong, H. Zhao, Global classical solutions to the one-dimensional compressible fluid models of Korteweg type with large initial data , J. Diff. Eqns., 259, no. 8 (2015), 4376–4411
2015
Later among the works it cites.
M. Gisclon and I. Lacroix-Violet, About the barotropic compressible quantum Navier-Stokes
2015
Later among the works it cites.
A. Jüngel and D. Matthes, The Derrida-Lebowitz-Speer-Spohn equation: existence, non-uniqueness, and decay rates of the solutions
2015
Later among the works it cites.
2015
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2012
Cited alongside, same era.
A. Jüngel, Dissipative quantum fluid models
2012
Cited alongside, same era.
A. Jüngel and J.P. Milisic, Quantum Navier-Stokes equations
2012
Cited alongside, same era.
D. Bresch, B. Desjardins, E. Zatorska, Two-velocity hydrodynamics in fluid mechanics: Part II. Existence of global κ − \kappa- entropy solutions to the compressible Navier-Stokes systems with degenerate viscosities , J. Math. Pures Appl., 104, no. 4 (2015), 801–836
2015
Cited alongside, same era.
D. Bresch, V. Giovangigli, E. Zatorska, Two-velocity hydrodynamics in fluid mechanics: Part I. Well posedness for zero Mach number systems , J. Math Pures Appl., 104, no. 4 (2015), 762–800
2015
Cited alongside, same era.
2015
Cited alongside, same era.
S. Benzoni-Gavage, Propagating phase boundaries and capillary fluids , available online at http://math.univ-lyon1.fr/~benzoni/Levico.pdf
Cited in the paper.
2015
Later among the works it cites.
2015
Later among the works it cites.
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
Closest in time.
P. Germain, P. LeFloch, The finite energy method for compressible fluids: The Navier-Stokes-Korteweg model , Comm. Pure Appl. Math., 69, no.1 (2016), 3–61
2016
Closest in time.
I. Lacroix-Violet, A. Vasseur, Global weak solutions to the compressible quantum navier-stokes equation and its semi-classical limit , arxiv.org:1607.06646, (2016)
2016
Closest in time.
C. Audiard, B. Haspot, Global well-posedness of the Euler-Korteweg system for small irrotational data , Comm. Math. Phys. 351
2017
Closest in time.
P. Antonelli and S. Spirito, On the compactness of finite energy weak solutions to the Quantum Navier-Stokes equations , J. Hyperbolic Differ. Equ., 15
2018
Closest in time.