典型文献
Scattering for 3D Cubic Focusing NLS on the Domain Outside a Convex Obstacle Revisited
文献摘要：
In this article,we consider the focusing cubic nonlinear Schr?dinger equation(NLS)in the exterior domain outside of a convex obstacle in R3 with Dirichlet boundary conditions.We revisit the scattering result below ground state in Killip-Visan-Zhang[The focusing cubic NLS on exterior domains in three dimensions.Appl.Math.Res.Express.AMRX,1,146-180(2016)]by utilizing the method of Dodson and Murphy[A new proof of scattering below the ground state for the 3d radial focusing cubic NLS.Proc.Amer.Math.Soc.,145,4859-4867(2017)]and the dispersive estimate in Ivanovici and Lebeau[Dispersion for the wave and the Schr?dinger equations outside strictly convex obstacles and counterexamples.Comp.Rend.Math.,355,774-779(2017)],which avoids using the concentration compactness.We conquer the difficulty of the boundary in the focusing case by establishing a local smoothing effect of the boundary.Based on this effect and the interaction Morawetz estimates,we prove that the solution decays at a large time interval,which meets the scattering criterion.
文献关键词：
中图分类号：
作者姓名：
Cheng Bin XU;Teng Fei ZHAO;Ji Qiang ZHENG
作者机构：
The Graduate School of China Academy of Engineering Physics,Beijing 100088,P.R.China;School of Mathematics and Physics,University of Science and Technology Beijing,Beijing 100083,P.R.China;Institute of Applied Physics and Computational Mathematics,P.O.Box 8009,Beijing 100088,P.R.China
文献出处：
引用格式：
[1]Cheng Bin XU;Teng Fei ZHAO;Ji Qiang ZHENG-.Scattering for 3D Cubic Focusing NLS on the Domain Outside a Convex Obstacle Revisited)[J].数学学报（英文版）,2022(06):1054-1068
A类：
Visan,AMRX,Dodson,Ivanovici,Lebeau,counterexamples,Rend,Morawetz
B类：
Scattering,Cubic,Focusing,NLS,Domain,Outside,Convex,Obstacle,Revisited,In,this,article,consider,focusing,cubic,nonlinear,Schr,dinger,exterior,outside,convex,R3,Dirichlet,boundary,conditions,We,revisit,scattering,result,below,ground,state,Killip,Zhang,domains,three,dimensions,Appl,Math,Res,Express,by,utilizing,method,Murphy,new,proof,3d,radial,Proc,Amer,Soc,dispersive,Dispersion,wave,equations,strictly,obstacles,Comp,which,avoids,concentration,compactness,conquer,difficulty,case,establishing,local,smoothing,effect,Based,interaction,estimates,prove,that,solution,decays,large,interval,meets,criterion
AB值：
0.556639
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