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In this note, we prove a blow-up result for a semilinear generalized Tricomiequation with nonlinear term of derivative type, i.e., for the equation$\mathscr{T}_{\!\!\ell} u = |\partial_t u|^p$, where $ \mathscr{T}_{\!\!\ell} =\partial_t^2-t^{2\ell}\Delta$. Smooth solutions blow up in finite time forpositive Cauchy data when the exponent $p$ of the nonlinear term is below$\frac{\mathscr{Q}}{\mathscr{Q}-2}$, where $\mathscr{Q}=(\ell+1)n+1$ is thequasi-homogeneous dimension of the generalized Tricomi operator$\mathscr{T}_{\!\!\ell}$. Furthermore, we get also an upper bound estimate forthe lifespan.

A blow-up result for a generalized Tricomi equation with nonlinearity of derivative type