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1. | Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic |
References:
[1] |
S. E. Bechtel, F. J. Rooney and M. G. Forest, Connection between stability, convexity of internal energy, and the second law for compressible Newtonian fuids, J. Appl. Mech., 72 (2005), 299-300.
doi: 10.1115/1.1831297. |
[2] |
E. Becker, "Gasdynamik," (German), Leitfäden der Angewandten Mathematik und Mechanik, Band 6, B. G. Teubner Verlagsgesellschaft, Stuttgart, 1966. |
[3] |
D. Bresch and B. Desjardins, On the existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids, J. Math. Pures Appl. (9), 87 (2007), 57-90.
doi: 10.1016/j.matpur.2006.11.001. |
[4] |
J. Carrillo, A. Jüngel, P. A. Markowich, G. Toscani and A. Unterreiter, Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities, Monatshefte Math., 133 (2001), 1-82.
doi: 10.1007/s006050170032. |
[5] |
C. M. Dafermos, The second law of thermodynamics and stability, Arch. Rational Mech. Anal., 70 (1979), 167-179.
doi: 10.1007/BF00250353. |
[6] |
B. Desjardins, Regularity of weak solutions of the compressible isentropic Navier-Stokes equations, Commun. Partial Differential Equations, 22 (1997), 977-1008. |
[7] |
R. J. DiPerna and P.-L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math., 98 (1989), 511-547.
doi: 10.1007/BF01393835. |
[8] |
S. Eliezer, A. Ghatak and H. Hora, "An Introduction to Equations of States, Theory and Applications," Cambridge University Press, Cambridge, 1986. |
[9] |
E. Feireisl and Novotný, Weak-strong uniqueness property for the full Navier-Stokes-Fourier system, Arch. Rational Mech. Anal., to appear, 2012. |
[10] |
E. Feireisl and A. Novotný, "Singular Limits in Thermodynamics of Viscous Fluids," Advances in Mathematical Fluid Mechanics, Birkhäuser Verlag, Basel, 2009. |
[11] |
E. Feireisl, A. Novotný and B. J. Jin, Relative entropies, suitable weak solutions, and uniqueness for the compressible Navier-Stokes system, J. Math. Fluid Mechanics, to appear, 2012. |
[12] |
E. Feireisl, A. Novotný and Y. Sun, Suitable weak solutions to the Navier-Stokes equations of compressible viscous fluids, Indiana Univ. Math. J., to appear, 2012. |
[13] |
E. Feireisl and D. Pražák, "Asymptotic Behavior of Dynamical Systems in Fluid Mechanics," AIMS Series on Applied Mathematics, 4, American Institute of Mathematical Sciences (AIMS), Springfield, MO, 2010. |
[14] |
P. Germain, Weak-strong uniqueness for the isentropic compressible Navier-Stokes system, J. Math. Fluid Mech., published online, 2010. |
[15] |
A. Mellet and A. Vasseur, Existence and uniqueness of global strong solutions for one-dimensional compressible Navier-Stokes equations,, SIAM J. Math. Anal., 39 (): 1344.
doi: 10.1137/060658199. |
[16] |
L. Saint-Raymond, Hydrodynamic limits: Some improvements of the relative entropy method, Annal. I. H. Poincaré Anal. Non Linéaire, 26 (2009), 705-744. |
show all references
References:
[1] |
S. E. Bechtel, F. J. Rooney and M. G. Forest, Connection between stability, convexity of internal energy, and the second law for compressible Newtonian fuids, J. Appl. Mech., 72 (2005), 299-300.
doi: 10.1115/1.1831297. |
[2] |
E. Becker, "Gasdynamik," (German), Leitfäden der Angewandten Mathematik und Mechanik, Band 6, B. G. Teubner Verlagsgesellschaft, Stuttgart, 1966. |
[3] |
D. Bresch and B. Desjardins, On the existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids, J. Math. Pures Appl. (9), 87 (2007), 57-90.
doi: 10.1016/j.matpur.2006.11.001. |
[4] |
J. Carrillo, A. Jüngel, P. A. Markowich, G. Toscani and A. Unterreiter, Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities, Monatshefte Math., 133 (2001), 1-82.
doi: 10.1007/s006050170032. |
[5] |
C. M. Dafermos, The second law of thermodynamics and stability, Arch. Rational Mech. Anal., 70 (1979), 167-179.
doi: 10.1007/BF00250353. |
[6] |
B. Desjardins, Regularity of weak solutions of the compressible isentropic Navier-Stokes equations, Commun. Partial Differential Equations, 22 (1997), 977-1008. |
[7] |
R. J. DiPerna and P.-L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math., 98 (1989), 511-547.
doi: 10.1007/BF01393835. |
[8] |
S. Eliezer, A. Ghatak and H. Hora, "An Introduction to Equations of States, Theory and Applications," Cambridge University Press, Cambridge, 1986. |
[9] |
E. Feireisl and Novotný, Weak-strong uniqueness property for the full Navier-Stokes-Fourier system, Arch. Rational Mech. Anal., to appear, 2012. |
[10] |
E. Feireisl and A. Novotný, "Singular Limits in Thermodynamics of Viscous Fluids," Advances in Mathematical Fluid Mechanics, Birkhäuser Verlag, Basel, 2009. |
[11] |
E. Feireisl, A. Novotný and B. J. Jin, Relative entropies, suitable weak solutions, and uniqueness for the compressible Navier-Stokes system, J. Math. Fluid Mechanics, to appear, 2012. |
[12] |
E. Feireisl, A. Novotný and Y. Sun, Suitable weak solutions to the Navier-Stokes equations of compressible viscous fluids, Indiana Univ. Math. J., to appear, 2012. |
[13] |
E. Feireisl and D. Pražák, "Asymptotic Behavior of Dynamical Systems in Fluid Mechanics," AIMS Series on Applied Mathematics, 4, American Institute of Mathematical Sciences (AIMS), Springfield, MO, 2010. |
[14] |
P. Germain, Weak-strong uniqueness for the isentropic compressible Navier-Stokes system, J. Math. Fluid Mech., published online, 2010. |
[15] |
A. Mellet and A. Vasseur, Existence and uniqueness of global strong solutions for one-dimensional compressible Navier-Stokes equations,, SIAM J. Math. Anal., 39 (): 1344.
doi: 10.1137/060658199. |
[16] |
L. Saint-Raymond, Hydrodynamic limits: Some improvements of the relative entropy method, Annal. I. H. Poincaré Anal. Non Linéaire, 26 (2009), 705-744. |
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