ArticleOriginal scientific text
Title
Some stability results for reactive Navier-Stokes-Poisson systems
Authors 1
Affiliations
- 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
- R. Kippenhahn and A. Weingert, Stellar structure and evolution, Springer, 1994.
- S. Chandrasekhar, An introduction to the study of stellar structure, Dover, 1957.
- 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.
- G.-Q. Chen, Global solution to the compressible Navier-Stokes equations for a reacting mixture, SIAM J. Math. Anal. 23 (1992), 609-634
- 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.
- 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).
- P. Ledoux and T. Walraven, Variable stars, Handbuch der Physik 51, 353-604, Springer, 1958.
- J. Bebernes and D. Eberly, Mathematical problems from combustion theory, Springer, 1989.
- P. Secchi, On the motion of gaseous stars in presence of radiation, Comm. Partial Diff. Equations 15 (1990), 185-204.
- S. N. Antonsev, A. V. Kazhikov and V. N. Monakhov, Boundary value problems in mechanics of nonhomogeneous fluids, North Holland, 1990.
- 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.
- B. Ducomet, Hydrodynamical models of gaseous stars, Reviews of Mathematical Physics 8 (1996), 957-1000.
- B. Ducomet, A remark about global existence for the Navier-Stokes-Poisson system, Applied Math. Letters 12 (1999), 31-37.
- 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.
- B. Ducomet, Some asymptotics for a reactive Navier-Stokes-Poisson system, Math. Models and Methods in Appl. Sci. 9 (1999), 1039-1076.
- V. A. Solonnikov, Evolution free boundary problem for equations of motion of viscous compressible self-gravitating fluid, SAACM 3 (1993), 257-275
- Z. Xin, Blow-up of smooth solutions to the compressible Navier-Stokes equations with compact density, Preprint Courant Institute, 1996.
- 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.
- 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.
- 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
- 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.
- S. Jiang, On initial boundary value problems for a viscous heat-conducting one-dimensional real gas, J. Differential Equations 110 (1994), 157-181.
- 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.
- S. Jiang, On the asymptotic behavior of the motion of a viscous heat-conducting one-dimensional real gas, Math. Z. 216 (1994), 317-336.
- 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,
- T. Luo, On the outer pressure problem of a viscous heat-conducting one-dimensional real gas, Acta Math. Appl. Sinica 13 (1997), 251-264.
- C. Dafermos and L. Hsiao, Global smooth thermomechanical processes in one-dimensional nonlinear thermoelasticity, Nonlinear Anal. Theory Methods Appl. 6 (1982), 435-454.
- M. Okada, Free boundary value problem for the equation of one-dimensional motion of viscous gas, Japan J. Appl. Math. 6 (1989), 161-177.
- T. Nagasawa, On the outer pressure problem of the one-dimensional polytropic ideal gas, Japan J. Appl. Math. 5 (1988), 53-85.
- 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.
- 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.
- H. Brézis, Analyse fonctionnelle, Masson, 1983.