ArticleOriginal scientific text

Title

Some stability results for reactive Navier-Stokes-Poisson systems

Authors 1

Affiliations

  1. Département de Physique Théorique et Appliquée, CEA Bruyères-le-Chatel, BP 12, F-91680, Bruyères-le-Chatel, France

Abstract

We review the main results concerning the global existence and the stability of solutions for some models of viscous compressible self-gravitating fluids used in classical astrophysics.

Bibliography

  1. R. Kippenhahn and A. Weingert, Stellar structure and evolution, Springer, 1994.
  2. S. Chandrasekhar, An introduction to the study of stellar structure, Dover, 1957.
  3. S. F. Shandarin and Ya. B. Zeldovitch, The large-scale structure of the universe: Turbulence, intermittency, structures in a self-gravitating medium, Reviews of Modern Physics 61 (1989), 185-220.
  4. G.-Q. Chen, Global solution to the compressible Navier-Stokes equations for a reacting mixture, SIAM J. Math. Anal. 23 (1992), 609-634
  5. E. Zadrzyńska and W. M. Zajączkowski, On global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting fluid, Preprint 523 of Institute of Mathematics of Polish Academy of Sciences, 1994.
  6. G. Ströhmer and W. M. Zajączkowski, On stability of certain equilibrium solution for compressible barotropic viscous self-gravitating fluid motions bounded by a free surface, Preprint, (1998).
  7. P. Ledoux and T. Walraven, Variable stars, Handbuch der Physik 51, 353-604, Springer, 1958.
  8. J. Bebernes and D. Eberly, Mathematical problems from combustion theory, Springer, 1989.
  9. P. Secchi, On the motion of gaseous stars in presence of radiation, Comm. Partial Diff. Equations 15 (1990), 185-204.
  10. S. N. Antonsev, A. V. Kazhikov and V. N. Monakhov, Boundary value problems in mechanics of nonhomogeneous fluids, North Holland, 1990.
  11. T. Makino and B. Perthame, Sur les solutions à symétrie sphériques de l'équation d' Euler-Poisson pour l'évolution d'étoiles gazeuses, Japan J. Appl. Math. 7 (1990), 165-170.
  12. B. Ducomet, Hydrodynamical models of gaseous stars, Reviews of Mathematical Physics 8 (1996), 957-1000.
  13. B. Ducomet, A remark about global existence for the Navier-Stokes-Poisson system, Applied Math. Letters 12 (1999), 31-37.
  14. B. Ducomet, A model of thermal dissipation for a one-dimensional viscous reactive and radiative gas, Math. Methods in Appl. Sci. 22 (1999), 1323-1349.
  15. B. Ducomet, Some asymptotics for a reactive Navier-Stokes-Poisson system, Math. Models and Methods in Appl. Sci. 9 (1999), 1039-1076.
  16. V. A. Solonnikov, Evolution free boundary problem for equations of motion of viscous compressible self-gravitating fluid, SAACM 3 (1993), 257-275
  17. Z. Xin, Blow-up of smooth solutions to the compressible Navier-Stokes equations with compact density, Preprint Courant Institute, 1996.
  18. H. Fujita-Yashima and R. Benabidallah, Spherically symmetric solutions of the Navier-Stokes equations for compressible isothermal flow with large discontinuous data, Indiana Univ. Math. J. 41 (1992), 1225-1301.
  19. D. Hoff, Equation à symétrie sphérique d'un gaz visqueux et calorifère avec la surface libre, Annali di Matematica Pura ed Applicata 168 (1995), 75-117.
  20. S. Jiang, Global spherically symmetric solutions to the equations of a viscous polytropic ideal gas in an exterior domain, Commun. Math. Phys. 178 (1996), 339-374
  21. B. Kawohl, Global existence of large solutions to initial boundary value problems for a viscous heat-conducting one-dimensional real gas, J. Differential Equations 58 (1985), 76-103.
  22. S. Jiang, On initial boundary value problems for a viscous heat-conducting one-dimensional real gas, J. Differential Equations 110 (1994), 157-181.
  23. S. Jiang, Remarks on the global existence in the dynamics of a viscous heat-conducting one-dimensional real gas, in: 'Qualitative aspects and applications of nonlinear evolution equations', H. Beirao da Veiga, T.-T. Li (eds.), World Scientific, 1994, 156-162.
  24. S. Jiang, On the asymptotic behavior of the motion of a viscous heat-conducting one-dimensional real gas, Math. Z. 216 (1994), 317-336.
  25. L. Hsiao and T. Luo, Large time behaviour of solutions for the outer pressure problem of a viscous heat-conducting one-dimensional real gas, Proc of the Royal Soc. of Edinburgh 126A (1996), 1277-1296,
  26. T. Luo, On the outer pressure problem of a viscous heat-conducting one-dimensional real gas, Acta Math. Appl. Sinica 13 (1997), 251-264.
  27. C. Dafermos and L. Hsiao, Global smooth thermomechanical processes in one-dimensional nonlinear thermoelasticity, Nonlinear Anal. Theory Methods Appl. 6 (1982), 435-454.
  28. M. Okada, Free boundary value problem for the equation of one-dimensional motion of viscous gas, Japan J. Appl. Math. 6 (1989), 161-177.
  29. T. Nagasawa, On the outer pressure problem of the one-dimensional polytropic ideal gas, Japan J. Appl. Math. 5 (1988), 53-85.
  30. B. Ducomet, On the stability of a stellar structure in one dimension II: The reactive case, Math. Modelling and Num. Anal. 31 (1997), 381-407.
  31. C. Dafermos, Global smooth solutions to the initial-boundary value problem for the equations of one-dimensional nonlinear thermoviscoelasticity, SIAM J. Math. Anal. 13 (1982), 397-408.
  32. H. Brézis, Analyse fonctionnelle, Masson, 1983.
Pages:
83-118
Main language of publication
English
Published
2000
Exact and natural sciences