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

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.