In this paper, the initial-boundary value problem of the original three-dimensional compressible Euler equations with (or without) time-dependent damping is considered. By considering a functional \(F(t,\alpha ,f)\) weighted by a general time-dependent parameter function \(\alpha \) and a general radius-dependent parameter function f, we show that if the initial value \(F|_{t=0}\) is sufficiently large, then the lifespan of the system is finite. Here, f can be any \(C^1\) strictly increasing function such that the sum of initial values of f and \(\alpha \) is non-negative. It follows that a class of conditions for non-existence of global classical solutions is established. Moreover, the conditions imply that a strong \(\alpha \) will lead to a more unrestrained necessary condition for classical solutions of the system to exist globally in time.

在本文中，考虑了带有（或不带有）时变阻尼的原始三维可压缩Euler方程的初边值问题。通过考虑由一般时间相关参数函数\（\ alpha \）和一般半径相关参数函数f加权的函数\（F（t，\ alpha，f）\），我们证明了如果初始值\ （F | _ {t = 0} \）足够大，则系统的寿命是有限的。在这里，f可以是任何\（C ^ 1 \）严格增加的函数，使得f和\（\ alpha \）的初始值之和是非负的。由此得出一类不存在全局经典解的条件。此外，条件暗示强\（\ alpha \）将导致系统经典解决方案在时间上全局存在的更为不受约束的必要条件。