Scattering Theory for the Defocusing Fourth Order NLS with Potentials

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 furth...

Full description

Saved in:
Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 34; no. 4; pp. 773 - 786
Main Authors Feng, Hong Liang, Wang, Hua, Yao, Xiao Hua
Format Journal Article
LanguageEnglish
Published Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.04.2018
Springer Nature B.V
Subjects
Defocusing
Estimates
Mathematics
Mathematics and Statistics
NLS;散布;散焦;相互作用;估计;操作员;衍生物;非线性
Scattering
Schrodinger equation
scattering
35P25
35Q55
potential
morawetz estimate
Fourth order NLS
47J35
Online AccessGet full text

Cover

More Information
Summary: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
Bibliography:Fourth order NLS, potential, morawetz estimate, scattering
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
11-2039/O1
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-018-7343-z