Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (6): 1851-1864.doi: 10.1016/S0252-9602(10)60178-6
• Articles • Previous Articles Next Articles
JIANG Song, OU Yao-Bin
Received:
2010-03-08
Online:
2010-11-20
Published:
2010-11-20
Supported by:
The research of Ou is partially supported by the China Postdoctoral Science Foundation (20090450333). Jiang is supported by the National Basic Research Program (2005CB321700) and NSFC (40890154).
CLC Number:
JIANG Song, OU Yao-Bin. A BLOW-UP CRITERION FOR COMPRESSIBLE VISCOUS HEAT-CONDUCTIVE FLOWS[J].Acta mathematica scientia,Series B, 2010, 30(6): 1851-1864.
[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 [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 [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. [17] Jiang S, Zhang P. Axisymmetric solutions of the 3-D Navier-Stokes equations for compressible isentropic fluids. [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 [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. [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 |
|