A NONLINEAR SCHRODINGER EQUATION WITH COULOMB POTENTIAL

作     者：苗长兴 张军勇 郑继强 Changxing MIAO;Junyong ZHANG;Jiqiang ZHENG

作者机构：Institute of Applied Physics and Computational MathematicsBeijing 100088China Department of MathematicsBeijing Institute of TechnologyBeijing 100081China Department of MathematicsCardiff UniversityUK 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2022年第42卷第6期

页      面：2230-2256页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：The authors were supported by NSFC(12126409,12026407,11831004) the J.Zheng was also supported by Beijing Natural Science Foundation(1222019)。 

主　　题：nonlinear Schrodinger equations long range potential global well-posedness blow-up scattering 

摘      要：In this paper,we study the Cauchy problem for the nonlinear Schrodinger equations with Coulomb potential i■_(t)u+△u+k/|x|u=λ/|u|^(p-l)u with 10,and the scattering theory when the Coulomb potential is repulsive,i.e.,when K≤O.The argument is based on the newlyestablished interaction Morawetz-type inequalities and the equivalence of Sobolev norms for the Laplacian operator with the Coulomb potential.