Author:
Ardila Alex H.,Murphy Jason
Abstract
AbstractWe consider the nonlinear Schrödinger equation in three space dimensions with a focusing cubic nonlinearity and defocusing quintic nonlinearity and in the presence of an external inverse-square potential. We establish scattering in the region of the mass-energy plane where the virial functional is guaranteed to be positive. Our result parallels the scattering result of [11] in the setting of the standard cubic-quintic NLS.
Publisher
Springer Science and Business Media LLC
Reference20 articles.
1. Bensouilah, A.: $$L^{2}$$ concentration of blow-up solutions for the mass-critical NLS with inverse-square potential, Preprint arXiv:1803.05944
2. Bourgain, J.: Global well-posedness of defocusing critical nonlinear Schrödinger equation in the radial case. J. Amer. Math. Soc. 12, 145–171 (1999)
3. Burq, N., Planchon, F., Stalker, J., Tahvildar-Zadeh, A.S.: Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential. J. Funct. Anal. 203, 519–549 (2003)
4. Christ, F., Weinstein, M.: Dispersion of small amplitude solutions of the generalized korteweg-de vries equation. J. Funct. Anal. 100, 87–109 (1991)
5. Colliander, J., Keel, M., Staffilani, G., Takaoka, H., Tao, T.: Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in $${\mathbb{R} }^{3}$$. Ann. Math. 167, 767–865 (2008)