|   [1]  Beale J T,  Kato T,  Majda A. Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Comm Math Phys, 1984, 94:  61--66 
[2]  Bourguignon J P,  Brezis H. Remarks on the Euler equation. J Funct Anal, 1974, 15: 341--363 
[3]  Cho Y,  Kim H.  Existence results for viscous polytropic fluids with vacuum. J Diff Eqns, 2006, 228:  377--411 
[4]  Desjardins B. Regularity of weak solutions of the compressible isentropic Navier-Stokes equations. Comm Partial Diff Eqns, 1997, 22:  977--1008 
[5]  Fan J, Jiang S. Blow-up criteria for the Navier-Stokes equations of compressible fluids. J Hyper Diff Eqns, 2008, 5: 167--185 
[6]  Fan J,  Jiang S,  Ni G. A blow-up criterion in terms of the density for compressible viscous flows. Preprint, 2009 
(www.math.ntnu.no/conservation/2009/060.html) 
[7]  Fan J,  Jiang S,  Ou Y. A blow-up criterion for three-dimensional compressible viscous flows. Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 2010, 27:  337--350 
[8]  Feireisl E,  Novotn\'{y} A, Petzeltová H. On the existence of globally defined weak solutions to the Navier-Stokes 
equations of isentropic compressible fluids. J Math Fluid Mech, 2001, 3:  358--392 
[9]  Feireisl E. Dynamics of Viscous Compressible Fluids. Oxford: Oxford Univ Press, 2004 
[10]  Feireisl E. On the motion of a viscous, compressible and heat conducting fluid. Indiana Univ Math J, 2004, 53:  1705--1738 
[11]  Haspot B. Regularity of weak solutions of the compressible isentropic Navier-Stokes equation. Preprint, arXiv:1001.1581v1, 2010. 
[12]  Hoff D. Discontinuous solutions of the Navier-Stokes equations for multidimensional flows of heat-conducting fluids. Arch Rat Mech Anal, 1997, 139: 303--354 
[13]  Hoff D. Compressible flow in a half-space with Navier boundary conditions. J Math Fluid Mech, 2005, 7: 315--338 
[14]  Huang X,  Xin Z. A blow-up criterion for classical solutions to the compressible Navier-Stokes equations. arXiv: 0903.3090 v2[math-ph]. 19 March, 2009 
[15] Jiang S. Global spherically symmetric solutions to the equations of a viscous polytropic ideal gas in an exterior domain. Comm Math Phys, 1996, 178: 339--374 
[16]  Jiang S, Zhang P. On spherically symmetric solutions of the compressible isentropic Navier-Stokes equations. 
Comm Math Phys, 2001, 215:  559--581 
[17]  Jiang S, Zhang  P. Axisymmetric solutions of the 3-D Navier-Stokes equations for compressible isentropic fluids. 
J Math Pure Appl, 2003, 82: 949--973 
[18]  Lions P L. Mathematical Topics in Fluid Mechanics, Vol 2. Oxford Lecture Series in Math and Its Appl 10. Oxford: Clarendon Press, 1998 
[19]  Matsumura A, Nishida T. The initial value problem for the equations of motion of viscous and heat-conductive gases. J Math Kyoto Univ, 1980, 20:  67--104 
[20]  Matsumura A, Nishida T. The initial boundary value problems for the equations of motion of compressible and 
heat-conductive fluids. Comm Math Phys, 1983, 89: 445--464 
[21]  Rozanova O. Blow up of smooth solutions to the compressible Navier-Stokes equations with the data highly decreasing at infinity. J Diff Eqns, 2008, 245: 1762--1774 
[22]  Sun Y, Wang C, Zhang Z. A Beale-Kato-Majda blow-up criterion for the 3-D compressible Navier-Stokes equations. 
Preprint, arXiv:1001.1247v1, 2010 
[23]  Triebel H. Interpolation Theory, Function Spaces, Differential Operators. 2nd ed. Heidelberg: Johann Ambrosius Barth, 1995 
[24]  Vagaint V A, Kazhikhov A V. On existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscous fluid. Siberian Math J, 1995, 36:  1108--1141 
[25]  Xin Z. Blow up of smooth solutions to the compressible Navier-Stokes equation with compact density. Comm Pure Appl Math, 1998, 51:  229--240   |