A note on spherically symmetric isentropic compressible flows with density-dependent viscosity coefficients
Tài liệu tham khảo
Bresch, 2003, On some compressible fluid models: Korteweg, lubrication, and shallow water systems, Comm. Partial Differential Equations, 28, 843, 10.1081/PDE-120020499
Bresch, 2003, Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model, Comm. Math. Phys., 238, 211, 10.1007/s00220-003-0859-8
Bresch, 2006, On the construction of approximate solutions for the 2D viscous shallow water model and for compressible Navier–Stokes models, J. Math. Pures Appl., 86, 362, 10.1016/j.matpur.2006.06.005
Bresch, 2007, On compressible Navier–Stokes equations with density dependent viscosities in bounded domains, J. Math. Pures Appl., 87, 227, 10.1016/j.matpur.2006.10.010
Chen, 2008, A vacuum problem for multidimensional compressible Navier–Stokes equations with degenerate viscosity coefficients, Commun. Pure Appl. Anal., 7, 987, 10.3934/cpaa.2008.7.987
Choe, 2003, Strong solutions of the Navier–Stokes equations for isentropic compressible fluids, J. Differential Equations, 190, 504, 10.1016/S0022-0396(03)00015-9
Danchin, 2000, Global existence in critical spaces for compressible Navier–Stokes equations, Invent. Math., 141, 579, 10.1007/s002220000078
Fang, 2004, Compressible Navier–Stokes equations with vacuum state in one dimension, Commun. Pure Appl. Anal., 3, 675, 10.3934/cpaa.2004.3.675
Feireisl, 2001, On the existence of globally defined weak solutions to the Navier–Stokes equations of isentropic compressible fluids, J. Math. Fluid Mech., 3, 358, 10.1007/PL00000976
Guo, 2008, Spherically symmetric isentropic compressible flows with density-dependent viscosity coefficients, SIAM J. Math. Anal., 39, 1402, 10.1137/070680333
Hoff, 1991, The failure of continuous dependence on initial data for the Navier–Stokes equations of compressible flow, SIAM J. Appl. Math., 51, 887, 10.1137/0151043
Hoff, 1992, Spherically symmetric solutions of the Navier–Stokes equations for compressible, isothermal flow with large, discontinuous initial data, Indiana Univ. Math. J., 41, 1225, 10.1512/iumj.1992.41.41060
Hoff, 2004, Symmetric nonbarotropic flows with large data and forces, Arch. Ration. Mech. Anal., 173, 297, 10.1007/s00205-004-0318-5
Jiang, 1998, Global smooth solutions of the equations of a viscous, heat-conducting one-dimensional gas with density-dependent viscosity, Math. Nachr., 190, 169, 10.1002/mana.19981900109
Jiang, 2001, Global spherically symmetric solutions of the compressible isentropic Navier–Stokes equations, Comm. Math. Phys., 215, 559, 10.1007/PL00005543
Jiang, 2003, Axisymmetric solutions of the 3D Navier–Stokes equations for compressible isentropic fluids, J. Math. Pure Appl., 82, 949, 10.1016/S0021-7824(03)00015-1
Jiang, 2005, Global weak solutions to 1D compressible isentropic Navier–Stokes with density-dependent viscosity, Methods Appl. Anal., 12, 239, 10.4310/MAA.2005.v12.n3.a2
Lions, 1998
Liu, 1998, Vacuum states of compressible flow, Discrete Continuous Dynam. Systems, 4, 1, 10.3934/dcds.1998.4.1
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
Mellet, 2007, On the barotropic compressible Navier–Stokes equation, Comm. Partial Differential Equations, 32, 431, 10.1080/03605300600857079
Salvi, 1993, Global existence for viscous compressible fluids and their behavior as t→∞, J. Fac. Sci. Univ. Tokyo Sect. IA, Math., 40, 17
Sun, 2006, Helical symmetry solutions of the 3-D Navier–Stokes equations for compressible isentropic fluids, J. Differential Equations, 222, 263, 10.1016/j.jde.2005.06.005
Xin, 1998, Blow-up of smooth solution to the compressible Navier–Stokes equations with compact density, Comm. Pure Appl. Math., 51, 229, 10.1002/(SICI)1097-0312(199803)51:3<229::AID-CPA1>3.0.CO;2-C
Yang, 2002, Compressible Navier–Stokes equations with degenerate viscosity coefficient and vacuum, Comm. Math. Phys., 230, 329, 10.1007/s00220-002-0703-6
Zhang, 2006, Global behavior of compressible Navier–Stokes equations with a degenerate viscosity coefficient, Arch. Ration. Mech. Anal., 182, 223, 10.1007/s00205-006-0425-6
Zhang, 2007, Global behavior of spherically symmetric Navier–Stokes equations with density-dependent viscosity, J. Differential Equations, 236, 293, 10.1016/j.jde.2007.01.025
T. Zhang, D.Y. Fang, Global behavior of spherically symmetric Navier–Stokes–Poisson system with degenerate viscosity coefficients, Arch. Ration. Mech. Anal. (in press)