In this paper, we study the blowup of smooth solutions to the compressible Euler equations with radial symmetry on some fixed bounded domains (\(B_{R}=\{x\in {\mathbb {R}}^{N}:\ |x|\le R\}\), \(N=1,2,\ldots \)) by introducing some new averaged quantities. We consider two types of flows: initially move inward and initially move outward on average. For the flow initially moving inward on average, we show that the smooth solutions will blow up in a finite time if the density vanishes at the origin only (\(\rho (t,0)=0,\ \rho (t,r)>0,\ 0<r\le R\)) for \(N\ge 1\) or the density vanishes at the origin and the velocity field vanishes on the two endpoints (\(\rho (t,0)=0,\ v(t,R)=0\)) for \(N=1\). For the flow initially moving outward, we prove that the smooth solutions will break down in a finite time if the density vanishes on the two endpoints (\(\rho (t,R)=0\)) for \(N=1\). The blowup mechanisms of the compressible Euler equations with constant damping or time-depending damping are obtained as corollaries.

在本文中，我们研究了在某些固定有界域上\（B_ {R} = \ {x \ in {\ mathbb {R}} ^ {N}：\\中的径向对称的可压缩Euler方程的光滑解的爆破| x | \ le R \} \），\（N = 1,2，\ ldots \））通过引入一些新的平均数量。我们考虑两种类型的流量：平均开始向内移动和初始向外移动。对于最初平均向内流动的流，我们表明，如果密度仅在原点处消失，则平滑解将在有限时间内爆炸（\（\ rho（t，0）= 0，\ \ rho（t，r ）> 0，\ 0 <r \ le R \））对于\（N \ ge 1 \）或密度在原点消失并且速度场在两个端点处消失（\（\ rho（t，0）= 0，\ v（t，R）= 0 \））\（N = 1 \）。对于最初向外流动的流，我们证明如果\（N = 1 \）的两个端点（\（\ rho（t，R）= 0 \）上的密度消失，则平滑解将在有限时间内分解。 ）。作为推论，获得了具有恒定阻尼或时变阻尼的可压缩Euler方程的爆破机理。