Critical exponent and sharp lifespan estimates for semilinear third‐order evolution equations

Abstract

We study semilinear third‐order (in time) evolution equations with fractional Laplacian and power nonlinearity , which was proposed by Bezerra–Carvalho–Santos (J. Evol. Equ. 2022) recently. In this manuscript, we obtain a new critical exponent for . Precisely, the global (in time) existence of small data Sobolev solutions is proved for the supercritical case , and energy solutions blow up in finite time even for small data if . Furthermore, to more accurately describe the blow‐up time, we derive new and sharp upper bound and lower bound estimates for the lifespan in the subcritical case and the critical case.