In this talk, we discuss the short pulse initial data (a class of large initial data) problem for some hyperbolic equations. Especially, for the 2D or 3D compressible isentropic Euler equations with damping and short pulse initial data $(\rho,u)(0,x)=(\bar\rho+\delta^{\nu}\rho_0(\frac{r-1}{\delta},\omega),\delta^{\nu}u_0 (\frac{r-1}{\delta}, \omega))$, we show that the global smooth solution exists when $\nu>1$, while the smooth solution can blow up in finite time when $0<\nu\le 1$. Therefore, $\nu=1$ is just the critical power of short pulse initial data for the global existence of smooth large solution. This is a joint work with Li Jintao and Prof.Ding Bingbing.