中文摘要：

详细讨论、分析了涉及灾害性天气预报的理论模式的稳定性，这些模式包括：非静力完全弹性方程组、滞弹性方程组．证明了非静力完全弹性方程组在无穷可微函数类中是稳定方程；滞弹性方程组则因为对流体的特殊假设，改变了连续方程的形式，于是出现了“流体为粘性与不可压假设的匹配”现象，从而使在实际预报工作中占有重要地位的这一类重要方程组与Navier-Stokes方程呈现了相同拓扑性质的不稳定性，而这是在数值预报工作中首先应该避免的．据此提出了如何修改应用模式的参考意见．

英文摘要：

Stability related to theoretical model for catastrophic weather prediction that includes nonhydrostatic perfect elastic model, anelastic model was discussed and analyzed in detail. It was proved that in infinitely differentiable function class non-hydrostatic perfect elastic equations set is stable. However, for anelastic equations set, its continuity equation is changed in form because of the parlicular hypothesis for fluid, so ＂the matching consisting of both viscosity coefficient and incompressible assumption＂ appears, thereby the most important equations set of this class in practical prediction shows the same instability in topological property as Navier-Stokes equation, which should be avoided first in practical numerical prediction. In light of this, the referenced suggestions to amend applied model are finally presented.