Scattering Theory for the Defocusing Fourth Order NLS with Potentials  

作　　者：Hong Liang FENG Hua WANG Xiao Hua YAO 

机构地区：[1]School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China [2]School of Mathematics and Statistics and Hubei Province Key Laboratory of Mathematical Physics, Central China Normal University, Wuhan 430079, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2018年第4期773-786,共14页数学学报（英文版）

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)

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. nBased 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

关 键 词：Fourth order NLS potential morawetz estimate SCATTERING 

分 类 号：O175[理学—数学]