[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 |