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On Global in Time Properties of the Symmetric Compressible Barotropic Navier–Stokes–Poisson Flows in a Vacuum

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Instability in Models Connected with Fluid Flows II

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References

  1. A. A. Amosov and A. A. Zlotnik, Global solvability of a class of quasilinear systems of composite type with nonsmooth data, Differ. Equ. 30(1994), 545-558.

    MathSciNet  Google Scholar 

  2. A. A. Amosov and A. A. Zlotnik, Semidiscrete method for solving the equations of a one-dimensional motion of a viscous heat-conducting gas with nonsmooth data. Regularity of solutions,Russian Math. 43(1999), no. 5, 10-23.

    MathSciNet  Google Scholar 

  3. J. Berg and J. Lofstrom, Interpolation Spaces. An Introduction, Springer, Berlin, 1975.

    Google Scholar 

  4. P. Billingsley, Convergence of Probability Measures, John Wiley and Sons, New York, 1968.

    MATH  Google Scholar 

  5. S. Chandrasekhar, An Introduction to the Study of Stellar Structures, Dover, New York, 1967.

    Google Scholar 

  6. P. H. Chavanis, Gravitational stability of isothermal and polytropic spheres, Astronom. Astrophys. 401(2003), 15-42.

    Article  MATH  Google Scholar 

  7. H.-Y. Chin, Stellar Physics.Vol. I. Blaisdell, Waltham, 1968.

    Google Scholar 

  8. B. Ducomet, Hydrodynamical models of gaseous stars, Rev.Math. Phys. 8(1996), 957-1000.

    Article  MATH  MathSciNet  Google Scholar 

  9. B. Ducomet and A. Zlotnik, Viscous compressible barotropic symmetric flows with free boundary under general mass force. Part I: Uniform-intime bounds and stabilization,Math. Methods Appl. Sci. 28(2005), 827-863.

    Article  MATH  MathSciNet  Google Scholar 

  10. H. Fujita-Yashima and N. Ablaoui-Lahmar, Sur l’expansion d’un gaz visqueux et calorif‘ere avec la surface libre en une dimension et ‘a symétrie sphérique, Atti Sem. Mat. Fiz. Univ. Modena 40(2001), 1-17.

    MathSciNet  Google Scholar 

  11. P. Haensel, J. L. Zdunik, and R. Schae.er, Phase transition in dense matter and radial pulsations of neutron stars, Astronom. Astrophys. 217(1989), 137-144.

    Google Scholar 

  12. P. Hartman, Ordinary Differential Equations, John Wiley and Sons, New York, 1964.

    MATH  Google Scholar 

  13. J. M. Heinzle and C. Uggla, Newtonian stellar models, Ann. Phys. 308(2003), 18-61.

    Article  MATH  MathSciNet  Google Scholar 

  14. J. M. Huntley and W. C. Saslaw, The distribution of stars in galactic nuclei: loaded polytropes, Astrophys. J. 199(1975), 328-335.

    Article  Google Scholar 

  15. W. C. Kuan and S. S. Lin, Numbers of equilibria for the equation of selfgravitating isentropic gas surrounding a solid ball, Japan J. Industrial Appl. Math. 13(1996), 311-331.

    MATH  MathSciNet  Google Scholar 

  16. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’ceva, Linear and Quasilinear Equations of Parabolic Type, Am. Math. Soc., Providence, R.I., 1968.

    Google Scholar 

  17. S. S. Lin, Stability of gaseous stars in spherically symmetric motions, SIAM J. Math. Anal. 28(1997), 539-569.

    Article  MATH  MathSciNet  Google Scholar 

  18. J.-L. Lions, Quelques Méthodes de Résolution des Probl‘emes aux Limites Non Linéaires, Dunod, Paris, 1969.

    Google Scholar 

  19. R. A. Lyttleton, The Ramsey phase-change hypothesis, The Moon the Planets 19(1978), 425-442.

    Article  Google Scholar 

  20. S. Matuŝu-Neĉasova ˆ, M. Okada, and T. Makino, Free boundary problem for the equation of spherically symmetric motion of a viscous gas. II, Japan J. Industrial Appl. Math. 12(1995), 195-203.

    Article  Google Scholar 

  21. S. Matuŝu-Neĉasova ˆ, M. Okada, and T. Makino, Free boundary problem for the equation of spherically symmetric motion of a viscous gas. III, Japan J. Industrial Appl. Math. 14(1997), 199-213.

    Google Scholar 

  22. I. Straŝkraba and A. Zlotnik, On a decay rate for 1D-viscous compressible barotropic fluid equations, J. Evolut. Equat. 2(2002), 69-96.

    Article  MATH  Google Scholar 

  23. I. Straŝkraba and A. Zlotnik, Global behavior of 1d-viscous compressible barotropic fluid with a free boundary and large data, J. Math. Fluid Mech. 5(2003), 119-143.

    MathSciNet  MATH  Google Scholar 

  24. G. Strömer and W. Zajaczkowski, On the existence and properties of the rotationally symmetric equilibrium states of compressible barotropic self-gravitating fluids, Indiana Univer. Math. J. 46(1997), 1181-1220.

    Google Scholar 

  25. G. Strömer and W. Zajaczkowski, Local existence of solutions of free boundary problem for the equations of compressible viscous selfgravitating fluids, Appl. Math. 26(1999), 1-31.

    MathSciNet  Google Scholar 

  26. A. A. Zlotnik, Uniform estimates and stabilization of symmetric solutions of a system of quasilinear equations, Di.er. Equ. 36(2000), 701-716.

    MATH  MathSciNet  Google Scholar 

  27. A. Zlotnik, Stress and heat .ux stabilization for viscous compressible medium equations with a nonmonotone equation of state, Appl. Math. Lett. 16(2003), 1231-1237.

    Article  MATH  MathSciNet  Google Scholar 

  28. A. A. Zlotnik and A. A. Amosov, Global generalized solutions of the equations of the one-dimensional motion of a viscous barotropic gas, Sov. Math. Dokl. 37(1988), 554-558.

    MATH  MathSciNet  Google Scholar 

  29. A. A. Zlotnik and B. Ducomet, Stabilization rate and stability for viscous compressible barotropic symmetric flows with a free boundary for a general mass force, Sb. Math. 196(2005), 1745-1799.

    Article  MathSciNet  MATH  Google Scholar 

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Zlotnik, A. (2008). On Global in Time Properties of the Symmetric Compressible Barotropic Navier–Stokes–Poisson Flows in a Vacuum. In: Bardos, C., Fursikov, A. (eds) Instability in Models Connected with Fluid Flows II. International Mathematical Series, vol 7. Springer, New York, NY. https://doi.org/10.1007/978-0-387-75219-8_7

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