带阻尼项的一维等熵欧拉方程组的爆破解

Blowup of Solutions to 1-D Isentropic Euler Equations with Damping

讨论了一维空间中带阻尼项的可压缩等熵欧拉方程组初值问题经典解的爆破.利用一维空间中欧拉方程组的局部解具有有限传播速度的性质,通过构造两类不同的泛函,证明当初始速度或初始动量的泛函足够大时,初值问题的经典解必定会在有限时间内爆破的结论.

The blowup of classical solutions for the initial value problem of the compressible isentropic Euler equation with damping in 1-dimensional space is discussed.Utilizing local solutions with finite propagation speed of nature of the Euler equation in one dimensional space,by constructing two different types of functional,the classical solutions of the initial value problem is proved to be blown up in finite time when the initial functional associated with the velocity or momentum is large enough.