摘要
Based on the endpoint Strichartz estimates for the fourth order SchrSdinger equation with potentials for n ≥ 5 by [Feng, H., Softer, A., Yao, X.： Decay estimates and Strichartz estimates of the fourth-order Schr6dinger 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 Schr6dinger 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 ＋ 8/n〈 p 〈 1 ＋ 8/n-4 in dimensions n ≥ 7. n
Based on the endpoint Strichartz estimates for the fourth order SchrSdinger equation with potentials for n ≥ 5 by [Feng, H., Softer, A., Yao, X.： Decay estimates and Strichartz estimates of the fourth-order Schr6dinger 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 Schr6dinger 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 ＋ 8/n〈 p 〈 1 ＋ 8/n-4 in dimensions n ≥ 7. n
基金
supported by the China National Science Foundation(Grant Nos.11371158 and 11771165)
the second author is supported by the China National Science Foundation(Grant Nos.11101172 and 11571131)
