带非线性阻尼项的欧拉——泊松方程组径向对称解的爆破问题

Blowup Phenomenon for the Radial Symmetric Solutions of the Compressible Euler-Poisson Equations with Nonlinear Damping

研究了N维空间中带非线性阻尼项的欧拉-泊松方程组的径向对称解的爆破问题.当t≥0时,定义了泛函H（t）和测试函数φ（r）,采用积分法得到了当H（0）满足一定条件时在非光滑边界条件下方程组的非平凡径向对称解将在有限时间内发生爆破.采用相似的方法也得到了一维空间中径向对称解的相应结论.

The blowup phenomenon of the Radial symmetric solutions for the N-dim com- pressible Euler-poisson equations with nonlinear damping is investigated. We first define the funtional H（t） and measurable testing function, where, Under certain condition for H（O）, We show that the nontrivial classical solutions will blowup result in the finite time by the integration. The corresponding blowup result for the 1-dim radial symmetric case is given in the same way.