Scattering for the mass super-critical perturbations of the mass critical nonlinear Schrödinger equations. (English) Zbl 1435.35344

Cheng, Xing

Ill. J. Math. 64, No. 1, 21-48 (2020).

Summary: We consider the Cauchy problem for the nonlinear Schrödinger (NLS) equation with double nonlinearities with opposite sign, with one term mass-critical and the other term mass-supercritical and energy-subcritical, which includes the well-known two-dimensional cubic-quintic NLS equation arising in the study of the boson gas with 2- and 3-body interactions. We prove global well-posedness and scattering in \(H^1(\mathbb{R}^d)\) below the threshold for nonradial data when \(1\le d\le 4\).

MSC:

35Q55	NLS equations (nonlinear Schrödinger equations)
35Q41	Time-dependent Schrödinger equations and Dirac equations
35L70	Second-order nonlinear hyperbolic equations
35P25	Scattering theory for PDEs
35A01	Existence problems for PDEs: global existence, local existence, non-existence
35A02	Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness

Keywords:

nonlinear Schrödinger (NLS) equation; lobal well-posedness; scattering

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