带阻尼项的三维等熵欧拉方程组解的爆破

Blowup for the Solutions of the 3-dimensional Isentropic Euler Equations With Damping

讨论三维空间中带线性阻尼项的等熵可压缩欧拉方程组,在假设某些初始数据较大的条件下,研究其初值问题经典解的爆破.一方面,利用对称双曲型方程组解的存在性理论,得到了三维空间中可压缩欧拉方程组的初值问题的经典解的局部存在性以及解的有限传播性质;另一方面,通过构造三个不同的泛函,当初始泛函足够大时得到了初值问题的经典解必定爆破的结论.

The blowup of classical solutions for the Cauchy problem of the 3-dimensional isentropic compressible Euler equations with linear damping is discussed under some hypotheses on the initial data. On the one hand,the local existence of the classical solutions is obtained and have limited speed by utilizing the theory for the quasi-linear symmetric hyperbolic systems. On the other hand,by constructing three different types of functional,it maintains that the classical solution of initial-value problem is proved to be blow up in finite time when the initial functional is large enough.