A Beale-Kato-Majda Criterion for Three Dimensional Compressible Viscous Heat-Conductive Flows

作者：Sun, Yongzhong^*; Wang, Chao; Zhang, Zhifei

来源：Archive for Rational Mechanics and Analysis, 2011, 201(2): 727-742.

DOI：10.1007/s00205-011-0407-1

• NAVIER-STOKES EQUATIONS
• BLOW-UP CRITERION
• CRITICAL SPACES
• FLUIDS
• REGULARITY
• EXISTENCE
• BOUNDARY
• MOTION
• GASES/

We prove a blow-up criterion in terms of the upper bound of (rho, rho (-1), theta) for a strong solution to three dimensional compressible viscous heat-conductive flows. The main ingredient of the proof is an a priori estimate for a quantity independently introduced in Haspot (Regularity of weak solutions of the compressible isentropic Navier-Stokes equation, arXiv:1001.1581, 2010) and Sun et al. (J Math Pure Appl 95:36-47, 2011), whose divergence can be viewed as the effective viscous flux.

• 出版日期2011-8
• 单位中国科学院数学与系统科学研究院; 南京大学; 北京大学