Some stability results for reactive Navier-Stokes-Poisson systems

B. Ducomet

Banach Center Publications (2000)

  • Volume: 52, Issue: 1, page 83-118
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Ducomet, B.. "Some stability results for reactive Navier-Stokes-Poisson systems." Banach Center Publications 52.1 (2000): 83-118. <http://eudml.org/doc/209065>.

@article{Ducomet2000,
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.},
author = {Ducomet, B.},
journal = {Banach Center Publications},
keywords = {global existence; stability; models of viscous compressible self-gravitating fluids},
language = {eng},
number = {1},
pages = {83-118},
title = {Some stability results for reactive Navier-Stokes-Poisson systems},
url = {http://eudml.org/doc/209065},
volume = {52},
year = {2000},
}

TY - JOUR
AU - Ducomet, B.
TI - Some stability results for reactive Navier-Stokes-Poisson systems
JO - Banach Center Publications
PY - 2000
VL - 52
IS - 1
SP - 83
EP - 118
AB - 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.
LA - eng
KW - global existence; stability; models of viscous compressible self-gravitating fluids
UR - http://eudml.org/doc/209065
ER -

References

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  1. [1] R. Kippenhahn and A. Weingert, Stellar structure and evolution, Springer, 1994. 
  2. [2] S. Chandrasekhar, An introduction to the study of stellar structure, Dover, 1957. Zbl0079.23901
  3. [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. [4] G.-Q. Chen, Global solution to the compressible Navier-Stokes equations for a reacting mixture, SIAM J. Math. Anal. 23 (1992), 609-634 Zbl0771.35044
  5. [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. Zbl0874.35097
  6. [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. [7] P. Ledoux and T. Walraven, Variable stars, Handbuch der Physik 51, 353-604, Springer, 1958. 
  8. [8] J. Bebernes and D. Eberly, Mathematical problems from combustion theory, Springer, 1989. Zbl0692.35001
  9. [9] P. Secchi, On the motion of gaseous stars in presence of radiation, Comm. Partial Diff. Equations 15 (1990), 185-204. Zbl0708.35096
  10. [10] S. N. Antonsev, A. V. Kazhikov and V. N. Monakhov, Boundary value problems in mechanics of nonhomogeneous fluids, North Holland, 1990. 
  11. [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. [12] B. Ducomet, Hydrodynamical models of gaseous stars, Reviews of Mathematical Physics 8 (1996), 957-1000. Zbl0949.76071
  13. [13] B. Ducomet, A remark about global existence for the Navier-Stokes-Poisson system, Applied Math. Letters 12 (1999), 31-37. 
  14. [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. Zbl1027.85005
  15. [15] B. Ducomet, Some asymptotics for a reactive Navier-Stokes-Poisson system, Math. Models and Methods in Appl. Sci. 9 (1999), 1039-1076. Zbl1035.76057
  16. [16] V. A. Solonnikov, Evolution free boundary problem for equations of motion of viscous compressible self-gravitating fluid, SAACM 3 (1993), 257-275 
  17. [17] Z. Xin, Blow-up of smooth solutions to the compressible Navier-Stokes equations with compact density, Preprint Courant Institute, 1996. 
  18. [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. [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. [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 Zbl0858.76069
  21. [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. Zbl0579.35052
  22. [22] S. Jiang, On initial boundary value problems for a viscous heat-conducting one-dimensional real gas, J. Differential Equations 110 (1994), 157-181. Zbl0805.35074
  23. [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. Zbl0835.35090
  24. [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. Zbl0807.35016
  25. [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, Zbl0864.35085
  26. [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. Zbl0910.76071
  27. [27] C. Dafermos and L. Hsiao, Global smooth thermomechanical processes in one-dimensional nonlinear thermoelasticity, Nonlinear Anal. Theory Methods Appl. 6 (1982), 435-454. Zbl0498.35015
  28. [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. Zbl0668.76081
  29. [29] T. Nagasawa, On the outer pressure problem of the one-dimensional polytropic ideal gas, Japan J. Appl. Math. 5 (1988), 53-85. Zbl0665.76076
  30. [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. Zbl0882.76025
  31. [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. Zbl0489.73124
  32. [32] H. Brézis, Analyse fonctionnelle, Masson, 1983. 

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