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In this paper we prove the existence of global strong solution for the Navier-Stokes equations with general degenerate viscosity coefficients.
O. A. Oleinik. On the uniqueness of the generalized solution of the Cauchy problem for a non-linear system of equations occurring in mechanics. Usp. Mat. Nauk
1957
Earlier work this paper cites.
Ya. I. Kanel. On a model system of equations of one-dimensional gas motion, Differ- entsial’nye Uravneniya
1968
Earlier work this paper cites.
S. Chapman and T.G Cowling. The mathematical theory of non-uniform gases. An account of the kinetic theory of viscosity, thermal conduction and diffusion in gases. Third edition, prepared in co-operation with D. Burnett. Cambridge University Press, London, 1970
1970
Earlier work this paper cites.
S. Kruzhkov. First-order quasilinear equations with several space variables. Mat. Sbornik
1970
Earlier work this paper cites.
A. V. Kazhikhov and V. V. Shelukhin. Unique global solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas. Prikl. Mat. Mech
1977
Earlier work this paper cites.
D. Serre. Solutions faibles globales des équations de Navier-Stokes pour un fluide compressible. C. R. Acad. Sci. Paris Sér. I Math
1986
Earlier work this paper cites.
D. Serre. Sur l’équation monodimensionnelle d’un fluide visqueux, compressible et conducteur de chaleur. C. R. Acad. Sci. Paris Sér. I Math
1986
Earlier work this paper cites.
D. Hoff. Global existence for 1D compressible, isentropic Navier-Stokes equations with large initial data. Trans. Amer. Math. Soc
1987
Earlier work this paper cites.
D. Hoff. Global solutions of the equations of one-dimensional, compressible flow with large data and forces, and with differing end states. Z. Angew. Math. Phys
1998
Earlier work this paper cites.
P-L. Lions. Mathematical topics in fluid mechanics. Vol. 2, Volume 10 of Oxford Lecture Series in Mathematics and its Applications
1998
Cited alongside, same era.
J.-F. Gerbeau and B. Perthame. Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation. Discrete Contin. Dyn. Syst. Ser. B
2001
Cited alongside, same era.
D. Hoff and J. Smoller. Non-formation of vacuum states for compressible Navier-Stokes equations. Comm. Math. Phys
2001
Cited alongside, same era.
D. Bresch and B. Desjardins. Existence of global weak solutions to the Navier- Stokes equations for viscous compressible and heat conducting fluids, Journal de Mathématiques Pures et Appliqués
2007
Cited alongside, same era.
A. Mellet and A. Vasseur. On the barotropic compressible Navier-Stokes equations. Comm. Partial Differential Equations
2007
R. Danchin, A Lagrangian approach for the compressible Navier-Stokes equations. Ann. Inst. Fourier
2014
Later among the works it cites.
B. Haspot. Hyperbolic Problems: Theory, Numerics, Applications Proceedings of the 14th International Conference on Hyperbolic Problems held in Padova, June 25-29, 2012, p. 667-674, 2014
2014
Later among the works it cites.
B. Haspot. New formulation of the compressible Navier-Stokes equations and parabolicity of the density. Preprint
2015
Later among the works it cites.
B. Haspot. From the highly compressible Navier-Stokes equations to fast diffusion and porous media equations, existence of global weak solution for the quasi-solutions. Journal of Mathematical Fluid Mechanics
2016
Later among the works it cites.
B. Haspot and E. Zatorska, From the highly compressible Navier-Stokes equations to the Porous Media equation, rate of convergence. To appear in Discrete and Continuous Dynamical Systems - Series A
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Cited alongside, same era.
A. Mellet and A. Vasseur. Existence and Uniqueness of global strong solutions for one-dimensional compressible Navier-Stokes equations. SIAM J. Math. Anal
2007
Cited alongside, same era.
Q. Jiu and Z. Xin. The Cauchy problem for 1D compressible flows with density-dependent viscosity coefficients. Kinet. Relat. Models
2008
Cited alongside, same era.
C. M. Dafermos. Hyperbolic Conservation Laws in Continuum Physics
2009
Cited alongside, same era.
D. Hoff and D. Serre. The Failure of Continuous Dependence on Initial Data for the Navier-Stokes Equations of Compressible Flow. SIAM Journal on Applied Mathematics
Cited in the paper.
2016
Later among the works it cites.
2018
Later among the works it cites.
B. Haspot. Existence of global strong solution for the compressible Navier-Stokes equations with degenerate viscosity coefficients in 1D. Mathematische Nachrichten
2018
Later among the works it cites.