带非线性阻尼项的三维空间等熵欧拉方程组解的爆破

The Blow-up of Three-Dimensional Isentropic Euler Equations with Nonlinear Damping Term

对某些初始数据较大的三维空间中带非线性阻尼项的欧拉方程组初值问题经典解的存在性进行研究.在经典解局部存在及具有有限传播速度的情况下,定义了三种不同泛函,均得到了其经典解在有限时间内必定发生爆破的结论.

In this paper,the existence of classical solutions for the initial value problem of Euler equations with nonlinear damping term in three-dimensional space with large initial data is studied.In the case of local existence of classical solutions and finite propagation velocity,three different functionals are defined,and the conclusion that the classical solution must blow up in finite time is obtained.