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On the expanding configurations of viscous radiation gaseous stars: the isentropic model. (English) Zbl 1418.35293

MSC:

35Q30 Navier-Stokes equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35Q35 PDEs in connection with fluid mechanics
35Q85 PDEs in connection with astronomy and astrophysics
76E20 Stability and instability of geophysical and astrophysical flows

Citations:

Zbl 1390.35246
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References:

[1] Auchmuty J F G and Beals R 1971 Variational solutions of some nonlinear free boundary problems Arch. Ration. Mech. Anal.43 255-71 · Zbl 0225.49013
[2] Caffarelli L A and Friedman A 1980 The shape of axisymmetric rotating fluid J. Funct. Anal.35 109-42 · Zbl 0439.35068
[3] Chandrasekhar S 1958 An Introduction to the Study of Stellar Structure (New York: Dover)
[4] Chanillo S and Li Y Y 1994 On diameters of uniformly rotating stars Commun. Math. Phys.166 417-30 · Zbl 0816.76076
[5] Chanillo S and Weiss G S 2012 A remark on the geometry of uniformly rotating stars J. Differ. Equ.253 553-62 · Zbl 1245.85001
[6] Coutand D, Lindblad H and Shkoller S 2010 A priori estimates for the free-boundary 3D compressible Euler equations in physical vacuum Commun. Math. Phys.296 559-87 · Zbl 1193.35139
[7] Coutand D and Shkoller S 2011 Well-posedness in smooth function spaces for moving-boundary 1D compressible Euler equations in physical vacuum Commun. Pure Appl. Math.64 328-66 · Zbl 1217.35119
[8] Coutand D and Shkoller S 2012 Well-posedness in smooth function spaces for the moving-boundary three-dimensional compressible Euler equations in physical vacuum Arch. Ration. Mech. Anal.206 515-616 · Zbl 1257.35147
[9] Deng Y, Liu T-P, Yang T and Yao Z-A 2002 Solutions of Euler-Poisson equations for gaseous stars Arch. Ration. Mech. Anal.164 261-85 · Zbl 1038.76036
[10] Federbush P, Luo T and Smoller J 2014 Existence of magnetic compressible fluid stars Arch. Ration. Mech. Anal.215 611-31 · Zbl 1308.35206
[11] Friedman A and Turkington B 1981 Existence and dimensions of a rotating white dwarf J. Differ. Equ.42 414-37 · Zbl 0493.76109
[12] Fu C-C and Lin S-S 1998 On the critical mass of the collapse of a gaseous star in spherically symmetric and isentropic motion Japan J. Ind. Appl. Math.15 461-9 · Zbl 0913.35108
[13] Hadžić M and Jang J 2017 Nonlinear stability of expanding star solutions of the radially symmetric mass-critical Euler-Poisson system Commun. Pure Appl. Math.71 827-91 · Zbl 1390.35246
[14] Hong G, Luo T and Zhu C 2018 Global solutions to physical vacuum problem of non-isentropic viscous gaseous stars and nonlinear asymptotic stability of stationary solutions J. Differ. Equ.265 177-236 · Zbl 1390.35363
[15] Jang J 2008 Nonlinear instability in gravitational Euler-Poisson systems for γ=65 Arch. Ration. Mech. Anal.188 265-307 · Zbl 1192.85003
[16] Jang J 2010 Local well-posedness of dynamics of viscous gaseous stars Arch. Ration. Mech. Anal.195 797-863 · Zbl 1197.35294
[17] Jang J 2014 Nonlinear instability theory of Lane-Emden stars Commun. Pure Appl. Math.67 1418-65 · Zbl 1309.35080
[18] Jang J and Makino T 2017 On slowly rotating axisymmetric solutions of the Euler-Poisson equations Arch. Ration. Mech. Anal.225 873-900 · Zbl 1375.35379
[19] Jang J and Masmoudi N 2009 Well-posedness for compressible Euler equations with physical vacuum singularity Commun. pure Appl. Math.62 1327-85 · Zbl 1213.35298
[20] Jang J and Masmoudi N 2015 Well-posedness of compressible Euler equations in a physical vacuum Commun. Pure Appl. Math.68 61-111 · Zbl 1317.35185
[21] Jang J and Tice I 2013 Instability theory of the Navier-Stokes-Poisson equations Anal. PDE6 1121-81 · Zbl 1284.35317
[22] Li Y Y 1991 On uniformly rotating stars Arch. Ration. Mech. Anal.115 367-93 · Zbl 0850.76784
[23] Lieb E H and Yau H-T 1987 The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics Commun. Math. Phys.112 147-74 · Zbl 0641.35065
[24] Lin S-S 1997 Stability of gaseous stars in spherically symmetric motions SIAM J. Math. Anal.28 539-69 · Zbl 0871.35012
[25] Lions P-L 1996 Mathematical Topics in Fluid Mechanics. Volume 1. Incompressible Models(Oxford Lecture Series in Mathematics and its Applications vol 3) (Oxford: Oxford University Press)
[26] Liu T-P 1996 Compressible flow with damping and vacuum Japan J. Ind. Appl. Math.13 25-32 · Zbl 0865.35107
[27] Liu X 2018 A model of radiational gaseous stars SIAM J. Math. Anal.50 6100-55 · Zbl 1423.76392
[28] Luo T and Smoller J 2004 Rotating fluids with self-gravitation in bounded domains Arch. Ration. Mech. Anal.173 345-77 · Zbl 1060.76125
[29] Luo T and Smoller J 2008 Nonlinear dynamical stability of Newtonian rotating and non-rotating white dwarfs and rotating supermassive stars Commun. Math. Phys.284 425-57 · Zbl 1166.35031
[30] Luo T and Smoller J 2009 Existence and nonlinear stability of rotating star solutions of the compressible Euler-Poisson equations Arch. Ration. Mech. Anal.191 447-96 · Zbl 1163.85001
[31] Luo T, Xin Z and Zeng H 2014 Well-posedness for the motion of physical vacuum of the three-dimensional compressible Euler equations with or without self-gravitation Arch. Ration. Mech. Anal.213 763-831 · Zbl 1309.35065
[32] Luo T, Xin Z and Zeng H 2016 Nonlinear asymptotic stability of the Lane-Emden solutions for the viscous gaseous star problem with degenerate density dependent viscosities Commun. Math. Phys.347 657-702 · Zbl 1351.35227
[33] Luo T, Xin Z and Zeng H 2016 On nonlinear asymptotic stability of the Lane-Emden solutions for the viscous gaseous star problem Adv. Math.291 90-182 · Zbl 1344.35150
[34] Luo T and Zeng H 2016 Global existence of smooth solutions and convergence to Barenblatt solutions for the physical vacuum free boundary Problem of compressible Euler equations with damping Commun. Pure Appl. Math.69 1354-96 · Zbl 1344.35086
[35] Rein G 2003 Nonlinear stability of gaseous stars Arch. Ration. Mech. Anal.168 115-30 · Zbl 1044.76026
[36] Strauss W A and Wu Y 2017 Steady states of rotating stars and galaxies SIAM J. Math. Anal.49 4865-914 · Zbl 1379.85006
[37] Wu Y 2015 On rotating star solutions to the non-isentropic Euler-Poisson equations J. Differ. Equ.259 7161-98 · Zbl 1333.35173
[38] Zeng H 2015 Global-in-time smoothness of solutions to the vacuum free boundary problem for compressible isentropic Navier-Stokes equations Nonlinearity28 331-45 · Zbl 1323.35222
[39] Zeng H 2017 Global resolution of the physical vacuum singularity for three-dimensional isentropic inviscid flows with damping in spherically symmetric motions Arch. Ration. Mech. Anal.226 33-82 · Zbl 1383.35150
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