In the present paper, we study the Cauchy problem for the weakly coupled system of the generalized Tricomi equations with multiple propagation speeds. Our aim of this paper is to prove a small data blow-up result and an upper estimate of lifespan of the problem for a suitable compactly supported initial data in the subcritical and critical cases of the Strauss type. The proof is based on the framework of the argument in the paper (Ikeda et al. in J Diff Equs 267:5165–5201, 2019). One of our new contributions is to construct two families of special solutions to the free equation (see (2.16) or (2.18)) as the test functions and prove their several properties. We emphasize that the system with two different propagation speeds is treated in this paper and the assumption on the initial data is improved from the point-wise positivity to the integral positivity.

在本文中，我们研究了具有多种传播速度的广义Tricomi方程的​​弱耦合系统的柯西问题。本文的目的是为了证明在Strauss类型的次临界和临界情况下，合适的紧凑支持初始数据的小数据爆炸结果和问题寿命的较高估计。证明基于论文中的论证框架（Ikeda等人，J Diff Equs 267：5165–5201，2019）。我们的新贡献之一是构造自由方程的两个特殊解族（请参阅（2.16）或（2.18））作为测试函数，并证明它们的若干性质。