Small data blow-up for the weakly coupled system of the generalized Tricomi equations with multiple propagation speeds

In the present paper, we study Cauchy problem for weakly coupled system of generalized Tricomi equations with multiple propagation speeds. Our aim this paper is to prove a small data blow-up result and an upper estimate lifespan suitable compactly supported initial in subcritical critical cases Strauss type. The proof based on framework argument [17]. One our new contributions construct two families special solutions free equation (see (2.16) or (2.18) as test functions their several properties. We emphasize that different speeds treated assumption improved from point-wise positivity integral positivity.