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

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.