Scattering Theory for the Defocusing Fourth Order NLS with Potentials

Based on the endpoint Strichartz estimates for the fourth order Schrödinger equation with potentials for n ≥ 5 by Feng, H., Soffer, A., Yao, X.: Decay estimates and Strichartz estimates of the fourth-order Schrödinger operator. J. Funct. Anal., 274, 605–658 (2018)], in this paper, the authors further derive Strichartz type estimates with gain of derivatives similar to the one in Pausader, B.: The cubic fourth-order Schrödinger equation. J. Funct. Anal., 256, 2473–2517 (2009)]. As their applications, we combine the classical Morawetz estimate and the interaction Morawetz estimate to establish scattering theory in the energy space for the defocusing fourth order NLS with potentials and pure power nonlinearity \(1 + \frac{8}{n} < p < 1 + \frac{8}{{n - 4}}\) in dimensions n ≥ 7.