三维可压缩Euler方程经典解的破裂  

Blow-up of Classical Solutions of Compressible Euler Equations in Three-dimensional Space

作　　者：张新丽[1] 

机构地区：[1]复旦大学数学研究所

出　　处：《复旦学报（自然科学版）》2005年第2期307-313,共7页Journal of Fudan University：Natural Science

基　　金：国家自然科学基金资助项目(10225102);教育部博士点基金;973计划"高维无穷维动力系统"

摘　　要：证明当可压缩的三维Euler方程具有球对称性质时,对初值的任何小扰动,经典解都在有限时间内破裂,并且给出了经典解的生命跨度的上界估计.It is studied that blow-up of classical solutions of compressible Euler equations in three-dimensional space with spherically symmetric initial data which is a small perturbation of amplitude ε from a constant state.It is proved that the classical solutions have to blow-up in finite time in spite of any small ε and an upper bound for the lifespan is obtained.

关 键 词：可压缩EULER方程 经典解 三维 对称性质 有限时间 上界估计 生命跨度 小扰动 内破裂 

分 类 号：O175.27[理学—数学] O186.12[理学—基础数学]