Sur la Régularité des Solutions faibles des Equations de Navier-Stokes isentropiques en dimension deux

Benoît Desjardins[1]

  • [1] D.M.I., École Normale Supérieure, FranceD.M.I., École Normale Supérieure, France

Séminaire Équations aux dérivées partielles (1997-1998)

  • Volume: 1997-1998, page 1-12

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Desjardins, Benoît. "Sur la Régularité des Solutions faibles des Equations de Navier-Stokes isentropiques en dimension deux." Séminaire Équations aux dérivées partielles 1997-1998 (1997-1998): 1-12. <http://eudml.org/doc/10953>.

@article{Desjardins1997-1998,
affiliation = {D.M.I., École Normale Supérieure, FranceD.M.I., École Normale Supérieure, France},
author = {Desjardins, Benoît},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {2D compressible Navier-Stokes equations; zero density; bounded density; regularity of weak solutions},
language = {fre},
pages = {1-12},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Sur la Régularité des Solutions faibles des Equations de Navier-Stokes isentropiques en dimension deux},
url = {http://eudml.org/doc/10953},
volume = {1997-1998},
year = {1997-1998},
}

TY - JOUR
AU - Desjardins, Benoît
TI - Sur la Régularité des Solutions faibles des Equations de Navier-Stokes isentropiques en dimension deux
JO - Séminaire Équations aux dérivées partielles
PY - 1997-1998
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 1997-1998
SP - 1
EP - 12
LA - fre
KW - 2D compressible Navier-Stokes equations; zero density; bounded density; regularity of weak solutions
UR - http://eudml.org/doc/10953
ER -

References

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  2. B. Desjardins, Linear transport equations with values in Sobolev spaces and application to the Navier-Stokes equations, Diff. and Int. Equ no 3 10 (1997) p. 577-586. Zbl0902.76028MR1744862
  3. B. Desjardins, Global existence results for the incompressible density dependant Navier-Stokes equations in the whole space, Diff. and Int. Equ (1997) no 3 10 p. 587-598. Zbl0902.76027MR1744863
  4. B. Desjardins, Regularity results for two dimensional viscous flows, Arch. for Rat. Mech. Anal. (1997) 137 p. 135-158. Zbl0880.76090MR1463792
  5. R. Coifman, P.L. Lions, Y. Meyer, S. Semmes, Compensated compactness and Hardy spaces, J. Math. Pures Appl., 72 (1993), p.247-286. Zbl0864.42009MR1225511
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  7. R.J. Di Perna, P.L. Lions, in preparation see also in Séminaire EDP 1988-1989, Ecole Polytechnique, Palaiseau, 1989. MR1032290
  8. D. Hoff, Global well-posedness of the Cauchy problem for nonisentropic gas dynamics with discontinuous data, J. Diff. Eq., 95 (1992), p.33-73. Zbl0762.35085MR1142276
  9. A.V. Kazhikov, V.V. Shelukhin, Unique global solution with respect to time of the initial boundary value problems for one dimensional equations of a viscous gas, J. Appl. Math. Mech., 41 (1977), p. 273-282. Zbl0393.76043MR468593
  10. P.L. Lions, Existence globale pour les equations de Navier-Stokes compressibles isentropiques, C.R. Acad. Sci. Paris, 316 (1993), p. 1335-1340. Zbl0778.76086MR1226126
  11. P.L. Lions, Compacité des solutions des équations de Navier-Stokes compressibles isentropiques, C.R. Acad. Sci. Paris, 317 (1993),p. 115-120. Zbl0781.76072MR1228976
  12. P.L. Lions, Mathematical Topics in Fluid Mechanics, Oxford University Press (1996). Zbl0866.76002MR1422251
  13. D. Serre, Solutions faibles globales des equations de Navier-Stokes pour un fluide compressible, C.R. Acad. Sci. Paris, 303 (1986), p. 629-642. Zbl0597.76067MR867555
  14. V.A. Solonnikov, Solvability of the initial boundary value problem fpr the equation of a viscous compressible fluid, J. Sov. Math., 14 (1980), p.1120-1133. Zbl0451.35092
  15. V.A. Vaigant, An example of the nonexistence with respect to time of the global solution of Navier-Stokes equations for a compressible viscous barotropic fluid. Dokl. Akad. Nauk339 (1994), no. 2, p. 155-156. Zbl0877.35092MR1316938
  16. A. Valli, W.M. Zajaczkowski, Navier-Stokes equations for compressible fluids : global existence and qualitative properties of the solutions in the general case, Comm. Math. Phys.103 (1986), p. 259-296. Zbl0611.76082MR826865

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