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arXiv:2310.18731 [math.AP]AbstractReferencesReviewsResources

Scattering and blow up for nonlinear Schrödinger equation with the averaged nonlinearity

Jumpei Kawakami

Published 2023-10-28Version 1

We consider 3-dimensional nonlinear Schr\"{o}dinger equation with an averaged nonlinearity. This is a generalized model of the resonant system of NLS with partial harmonic oscillator, in terms of the nonlinear power. We give a new proof for the conservation law of Kinetic energy and remove a restriction on the nonlinearity. Moreover, in the focusing, super-quintic, and sub-nonic case, we construct a ground state solution and classify the behavior of the solutions below the ground state. We show the sharp threshold for scattering and blow up.

Comments: 42 pages
Categories: math.AP
Subjects: 35Q55
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