Global solutions to compressible Navier–Stokes equations with spherical symmetry and free boundary

Liu, 1996, Compressible flow with damping and vacuum, Japan J. Indust. Appl. Math., 13, 25, 10.1007/BF03167296 Coutand, 2010, A priori estimates for the free-boundary 3D compressible Euler equations in physical vacuum, Comm. Math. Phys., 296, 559, 10.1007/s00220-010-1028-5 Coutand, 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, 10.1007/s00205-012-0536-1 Coutand, 2011, Well-posedness in smooth function spaces for moving-boundary 1-D compressible Euler equations in physical vacuum, Comm. Pure Appl. Math., LXIV, 0328, 10.1002/cpa.20344 Gu, 2012, Well-posedness of 1-D compressible Euler–Poisson equations with physical vacuum, J. Differ. Equ., 252, 2160, 10.1016/j.jde.2011.10.019 Gu, 2016, Local well-posedness of the three dimensional compressible Euler-Poisson equations with physical vacuum, J. Math. Pures Appl., 105, 662, 10.1016/j.matpur.2015.11.010 Jang, 2009, Well-posedness for compressible Euler equations with physical vacuum singularity, Commun. Pure Appl. Math., LXII, 1327, 10.1002/cpa.20285 Jang, 2015, Well-posedness of compressible Euler equations in a physical vacuum, Comm. Pure Appl. Math., LXVIII, 0061, 10.1002/cpa.21517 Luo, 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, 10.1007/s00205-014-0742-0 Jang, 2010, Local well-posedness of dynamics of viscous gaseous stars, Arch. Ration. Mech. Anal., 195, 797, 10.1007/s00205-009-0253-6 M. Hadzic, J. Jang, (2016) Expanding large global solutions of the equations of compressible fluid mechanics, arXiv:1610.01666. Hadžić, 2017, Nonlinear stability of expanding star solutions of the radially symmetric mass-critical Euler-Poisson system, Comm. Pure Appl. Math., 1 Luo, 2015, Global existence of smooth solutions and convergence to barenblatt solutions for the physical vacuum free boundary problem of compressible Euler equations with damping, Comm. Pure Appl. Math. Zeng, 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, 10.1007/s00205-017-1128-x Luo, 2016, On nonlinear asymptotic stability of the Lane-Emden solutions for the viscous gaseous star problem, Adv. Math., 291, 90, 10.1016/j.aim.2015.12.022 Luo, 2016, Nonlinear asymptotic stability of the Lane-Emden solutions for the viscous gaseous star problem with degenerate density dependent viscosities, Comm. Math. Phys., 347, 657, 10.1007/s00220-016-2753-1 Zeng, 2015, Global-in-time smoothness of solutions to the vacuum free boundary problem for compressible isentropic Navier–Stokes equations, Nonlinearity, 28, 331, 10.1088/0951-7715/28/2/331 Luo, 2000, Interface behavior of compressible Navier-Stokes equations with vacuum, SIAM J. Math. Anal., 31, 1175, 10.1137/S0036141097331044 Guo, 2012, Lagrange structure and dynamics for solutions to the spherically symmetric compressible Navier-Stokes equations, Comm. Math. Phys., 309, 371, 10.1007/s00220-011-1334-6 Li, 2016, Global strong solutions to radial symmetric compressible Navier-Stokes equations with free boundary, J. Differ. Equ., 261, 6341, 10.1016/j.jde.2016.08.038 Yeung, 2011, Analytical solutions to the Navier-Stokes-Poisson equations with density-dependent viscosity and with pressure, Proc. Amer. Math. Soc., 139, 3951, 10.1090/S0002-9939-2011-11048-7 Guo, 2012, Analytical solutions to the compressible Navier-Stokes equations with density-dependent viscosity coefficients and free boundaries, J. Differ. Equ., 253, 1, 10.1016/j.jde.2012.03.023 Zadrzyńska, 2001, Evolution free boundary problem for equations of viscous compressible heat-conducting capillary fluids, Math. Methods Appl. Sci., 24, 713, 10.1002/mma.238 Zadrzyńska, 1999, On nonstationary motion of a fixed mass of a viscous compressible barotropic fluid bounded by a free boundary, Colloq. Math., 79, 283, 10.4064/cm-79-2-283-310 Zaja̧czkowski, 1994, On nonstationary motion of a compressible barotropic viscous capillary fluid bounded by a free surface, SIAM J. Math. Anal., 25, 1, 10.1137/S0036141089173207 Zaja̧czkowski, 1993 Serrin, 1959, On the uniqueness of compressible fluid motions, Arch. Ration. Mech. Anal., 3–3, 271, 10.1007/BF00284180 Itaya, 1971, On the Cauchy problems for the system of fundamental equations describing the movement of compressible viscous fluid, Kodai Math. Sem. Rep., 23, 60, 10.2996/kmj/1138846265 Tani, 1977, On the first initial-boundary value problem of compressible viscous fluid motion, Publ. Res. Inst. Math. Sci., 13, 193, 10.2977/prims/1195190106 Tani, 1986, The initial value problem for the equations of the motion of compressible viscous fluid with some slip boundary condition, 675 Matsumura, 1980, The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ., 20, 67, 10.1215/kjm/1250522322 Matsumura, 1983, Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids, Comm. Math. Phys., 89, 445, 10.1007/BF01214738 Xin, 1998, Blowup of smooth solutions to the compressible Navier-Stokes equation with compact density, Comm. Pure Appl. Math., LI, 229, 10.1002/(SICI)1097-0312(199803)51:3<229::AID-CPA1>3.0.CO;2-C Xin, 2013, On blowup of classical solutions to the compressible Navier-Stokes equations, Comm. Math. Phys., 321, 529, 10.1007/s00220-012-1610-0 Cho, 2006, Blow-up of viscous heat-conducting compressible flows, J. Math. Anal. Appl., 320, 819, 10.1016/j.jmaa.2005.08.005 Cho, 2006, On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities, Manuscripta Math., 120, 91, 10.1007/s00229-006-0637-y Cho, 2006, Existence results for viscous polytropic fluids with vacuum, J. Differ. Equ., 228, 377, 10.1016/j.jde.2006.05.001 T. Zhang, D. Fang, Existence and uniqueness results for viscous, heat-conducting 3-D fluid with vacuum, 2007, arXiv:0702170. Huang, 2012, Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations, Comm. Pure Appl. Math., 65, 549, 10.1002/cpa.21382 Liu, 1997, Vacuum states for compressible flow, Discrete Contin. Dyn. Syst., 4, 1, 10.3934/dcds.1996.2.1 Solonnikov, 1992, A problem with free boundary for the Navier-Stokes equaitons for a compressible fluid in the presence of surface tension, J. Sov. Math., 62, 2814, 10.1007/BF01671006 Zadrzyśka, 1994, On local motion of a general compressible viscous heat conducting fluid bounded by a free surface, Ann. Pol. Math., LIX, 133, 10.4064/ap-59-2-133-170 Zaja̧czkowski, 1995, Existence of local solutions for free boundary problems for viscous compressible barotropic fluids, Ann. Pol. Math., LX, 255, 10.4064/ap-60-3-255-287 Zhang, 2009, Global behavior of spherically symmetric Navier-Stokes-Poisson system with degenerate viscosity coefficients, Arch. Ration. Mech. Anal., 191, 195, 10.1007/s00205-008-0183-8 Jang, 2011, Vacuum in gas and fluid dynamics, Vol. 153, 315 Okada, 1989, Free boundary value problems for the equation of one-dimensionai motion of viscous gas, Japan J. Appl. Math., 6, 161, 10.1007/BF03167921 Okada, 2004, Free boundary problem for one-dimensional motions of compressible gas and vacuum, Japan J. Indust. Appl. Math., 21, 109, 10.1007/BF03167467 Ou, 2015, Global strong solutions to the vacuum free boundary problem for compressible Navier-Stokes equations with degenerate viscosity and gravity force, J. Differ. Equ., 259, 6803, 10.1016/j.jde.2015.08.008 Zhang, 2009, A note on spherically symmetric isentropic compressible flows with density-dependent viscosity coefficients, Nonlinear Anal. RWA, 10, 2272, 10.1016/j.nonrwa.2008.04.014