Sharp lifespan estimates for subcritical generalized semilinear Tricomi equations

Abstract

In this paper, we investigate the Cauchy problem of the subcritical semilinear generalized Tricomi equations with dimension n ≥ 3. Under the assumption that the initial data are smooth and compactly supported, the Cauchy problem is shown to be locally well‐posed and the lower bound estimate of the lifespan is established. We also obtain the upper bound of the lifespan with the same scale; hence, the sharp lifespan is determined. The proof is based on the improved versions of the weighted Strichartz estimates.