A Model of Radiational Gaseous Stars

We introduce a model concerning radiational gaseous stars and establish the existence theory of stationary solutions to the free boundary problem of hydrostatic equations describing the radiative equilibrium. We also concern the local well-posedness of the moving boundary problem of the corresponding Navier-Stokes-Fourier-Poisson system and construct a prior estimates of strong and classical solutions. Our results explore the vacuum behaviour of density and temperature near the free boundary for the equilibrium and capture such degeneracy in the evolutionary problem.

[1]  On the critical mass of the collapse of a gaseous star in spherically symmetric and isentropic motion , 1998 .

[2]  Z. Xin,et al.  Well-Posedness for the Motion of Physical Vacuum of the Three-dimensional Compressible Euler Equations with or without Self-Gravitation , 2014, 1402.3640.

[3]  Juhi Jang,et al.  Local Well-Posedness of Dynamics of Viscous Gaseous Stars , 2007, 0706.1605.

[4]  Z. Xin,et al.  Nonlinear Asymptotic Stability of the Lane-Emden Solutions for the Viscous Gaseous Star Problem with Degenerate Density Dependent Viscosities , 2015, 1507.01069.

[5]  Rotating Fluids with Self-Gravitation in Bounded Domains , 2004, gr-qc/0501044.

[6]  T. Makino.  On spherically symmetric motions of a gaseous star governed by the Euler-Poisson equations , 2012, 1210.5769.

[7]  Song-Sun Lin,et al.  Stability of gaseous stars in spherically symmetric motions , 1997 .

[8]  S. Shkoller,et al.  Well-Posedness in Smooth Function Spaces for the Moving-Boundary Three-Dimensional Compressible Euler Equations in Physical Vacuum , 2012 .

[9]  Tai-Ping Liu,et al.  Compressible flow with damping and vacuum , 1996 .

[10]  A. Friedman.  Variational principles and free-boundary problems , 1982 .

[11]  Huihui Zeng.  Global-in-time smoothness of solutions to the vacuum free boundary problem for compressible isentropic Navier–Stokes equations , 2015 .

[12]  Existence and dimensions of a rotating white dwarf , 1981 .

[13]  On the Existence of Positive Radial Solutions for Nonlinear Elliptic Equations in Annular Domains , 2003 .

[14]  E. Lieb,et al.  Analysis, Second edition , 2001 .

[15]  Huihui Zeng.  Global Solutions to the Gas-Vacuum Interface Problem of Isentropic Compressible Inviscid Flows with Damping in Spherically Symmetric Motions and Physical Vacuum , 2014, 1410.8471.

[16]  E. Lieb,et al.  The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics , 1987 .

[17]  J. Smoller,et al.  Nonlinear Dynamical Stability of Newtonian Rotating and Non-rotating White Dwarfs and Rotating Supermassive Stars , 2007, 0710.3150.

[18]  Z. Xin,et al.  On Nonlinear Asymptotic Stability of the Lane-Emden Solutions for the Viscous Gaseous Star Problem , 2015, 1506.03906.

[19]  Non-Linear Stability of Gaseous Stars , 2002, math-ph/0210045.

[20]  Existence of Magnetic Compressible Fluid Stars , 2014, 1402.0265.

[21]  H. Poincaré,et al.  Les Méthodes nouvelles de la Mécanique céleste and An Introduction to the Study of Stellar Structure , 1958 .

[22]  S. Shkoller,et al.  Well‐posedness in smooth function spaces for moving‐boundary 1‐D compressible euler equations in physical vacuum , 2009, 1003.4721.

[23]  G. Weiss,et al.  A remark on the geometry of uniformly rotating stars , 2011, 1109.3046.

[24]  Mahir Hadžić,et al.  Nonlinear Stability of Expanding Star Solutions of the Radially Symmetric Mass‐Critical Euler‐Poisson System , 2016, 1605.08083.

[25]  Yilun Wu.  On rotating star solutions to non-isentropic Euler-Poisson equations , 2013, 1309.0175.

[26]  J. Jang.  Nonlinear Instability Theory of Lane‐Emden Stars , 2012, 1211.2463.

[27]  Zhen Lei,et al.  Local Well-posedness of the three dimensional compressible Euler--Poisson equations with physical vacuum , 2014, 1405.4612.

[28]  S. Shkoller,et al.  Communications in Mathematical Physics A Priori Estimates for the Free-Boundary 3 D Compressible Euler Equations in Physical Vacuum , 2009 .

[29]  Existence and Non-linear Stability of Rotating Star Solutions of the Compressible Euler–Poisson Equations , 2007, gr-qc/0703033.

[30]  T. Luo,et al.  Global Existence of Smooth Solutions and Convergence to Barenblatt Solutions for the Physical Vacuum Free Boundary Problem of Compressible Euler Equations with Damping , 2014, 1407.6111.

[31]  Juhi Jang,et al.  Instability theory of the Navier–Stokes–Poisson equations , 2011, 1105.5128.

[32]  Zhen Lei,et al.  Well-posedness of 1-D compressible Euler-Poisson equations with physical vacuum , 2011, 1105.0529.

[33]  R. Beals,et al.  Variational solutions of some nonlinear free boundary problems , 1971 .

[34]  Yanyan Li.  On uniformly rotating stars , 1991 .

[35]  W. Mccrea.  An Introduction to the Study of Stellar Structure , 1939, Nature.

[36]  J. Jang.  Nonlinear Instability in Gravitational Euler–Poisson Systems for $$\gamma=\frac{6}{5}$$ , 2008 .

[37]  Song-Sun Lin,et al.  Numbers of equilibria for the equation of self-gravitating isentropic gas surrounding a solid ball , 1996 .

[38]  Yanyan Li,et al.  On diameters of uniformly rotating stars , 1994 .

[39]  Juhi Jang,et al.  Well‐posedness of Compressible Euler Equations in a Physical Vacuum , 2010, 1005.4441.

[40]  Tai-Ping Liu,et al.  Solutions of Euler-Poisson Equations¶for Gaseous Stars , 2002 .