n维欧拉方程组初边值问题经典解的爆破

Blowup of the Classical Solutions for the IBVP of the n-dimensional Euler Equations

讨论了n维空间中带线性阻尼项的等熵欧拉方程组初边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n维空间中可压缩欧拉方程组的初边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,通过构造几种不同类型的泛函,证明了当初始数据较大时初边值问题的经典解必定在有限时间内爆破的结论。

This paper discusses the blowup of classical solutions for the initial-boundary value problem of the isentropic Euler equations with linear damping in n-dimensional space. On the one hand,the local existence of the classical solutions is obtained and has limited speed by utilizing the theory for the quasi-linear symmetric hyperbolic systems. On the other hand,by constructing several different types of functional,the classical solution of initialboundary value problem is proved to be blown up in finite time when the initial functional is large enough.