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
主讲：中国科学院 李竞副研究员
主办：数学与计算机科学学院
专家简介：李竞，男，博士，现任中国科学院数学与系统爱体育在线(中国)股份有限公司官网院基地副研究员。于厦门大学数学系获理学学士和硕士学位，香港中文大学数学系获博士学位。2004年至2006年于中国科学院数学与系统爱体育在线(中国)股份有限公司官网院应用数学所从事博士后研究，2006年至2008年于日本大阪大学从事JSPS博士后研究。研究领域涵盖流体力学的数学理论，主要包括可压缩Navier-Stokes方程及其相关的模型方程解的适定性理论，在“J.Differential Equations”,“J.Math.Pure Appl.”，“Commun.Math.Phys.”等国内外重要刊物发表学术论文十余篇，主持国家自然科学基金青年基金一项，国家自然科学基金面上项目一项。
报告摘要：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.