In this paper,we show the scattering of the radial solution for the nonlinear Schrodinger equation with combined power-type and Choquard-type nonlinearities iut+△u=λ1|u|p1-1u+λ2(Iα*|u|^(p2))|u|p^(2-2)u.in the ener...In this paper,we show the scattering of the radial solution for the nonlinear Schrodinger equation with combined power-type and Choquard-type nonlinearities iut+△u=λ1|u|p1-1u+λ2(Iα*|u|^(p2))|u|p^(2-2)u.in the energy space H^(1)(R^(N))forλ_(1)λ_(2)=-1.We establish a scattering criterion for radial solution together with Morawetz estimate which implies the scattering theory.Results show that the defocusing perturbation terms does not determine the scattering solution in energy space.展开更多
In this article,we consider the focusing cubic nonlinear Schr?dinger equation(NLS)in the exterior domain outside of a convex obstacle in R3with Dirichlet boundary conditions.We revisit the scattering result below grou...In this article,we consider the focusing cubic nonlinear Schr?dinger equation(NLS)in the exterior domain outside of a convex obstacle in R3with 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.展开更多
文摘In this paper,we show the scattering of the radial solution for the nonlinear Schrodinger equation with combined power-type and Choquard-type nonlinearities iut+△u=λ1|u|p1-1u+λ2(Iα*|u|^(p2))|u|p^(2-2)u.in the energy space H^(1)(R^(N))forλ_(1)λ_(2)=-1.We establish a scattering criterion for radial solution together with Morawetz estimate which implies the scattering theory.Results show that the defocusing perturbation terms does not determine the scattering solution in energy space.
基金Supported by Beijing Natural Science Foundation 1222019,PFCAEP project(Grant No.YZJJLX201901)NSFC(Grant No.11901041,12101040)NSAF(Grant No.U1530401)。
文摘In this article,we consider the focusing cubic nonlinear Schr?dinger equation(NLS)in the exterior domain outside of a convex obstacle in R3with 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.
