中国科学院数学与系统科学研究院
报告题目：Serrin-type blowup criteria for compressible Navier-Stokes equations
时 间：2013年3月26日（星期二）上午9:30-10:30
地 点：成功楼603教室
参加对象：数计学院函数论、方程相关教师和研究生
摘 要：
We will talk about a blowup criterion for the three-dimensional full compressible Navier-Stokes system describing the motion of a viscous, compressible, and heat conducting fluid. It is essentially shown that for the Cauchy problem and the initial-boundary-value one of the three-dimensional compressible flows with initial density allowed to vanish, the strong or smooth solution exists globally if the density is bounded from above and the velocity satisfies the Serrin's condition. Therefore, if the Serrin norm of the velocity remains bounded, it is not possible for other kinds of singularities (such as vacuum states vanish or vacuum appears in the non-vacuum region or even milder singularities) to form before the density becomes unbounded. This criterion is analogous to the well-known Serrin's blowup criterion for the three-dimensional incompressible Navier-Stokes equations, in particular, it is independent of the temperature and is just the same as that of the barotropic compressible Navier-Stokes equations.
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