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arXiv · 2209.01600

Scattering for non-radial 3D NLS with combined nonlinearities: the interaction Morawetz approach

Jacopo Bellazzini·Van Duong Dinh·Luigi Forcella
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Abstract

We give a new proof of the scattering below the ground state energy level for a class of nonlinear Schr\"odinger equations (NLS) with mass-energy intercritical competing nonlinearities. Specifically, the NLS has a focusing leading order nonlinearity with a defocusing perturbation. Our strategy combines interaction Morawetz estimates \`a la Dodson-Murphy and a new crucial bound for the Pohozaev functional of localized functions, which is essential to overcome the lack of a monotonicity condition. Furthermore, we give the rate of blow-up for symmetric solutions.

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Jacopo Bellazzini, Van Duong Dinh, Luigi Forcella. 2022-09-04. Scattering for non-radial 3D NLS with combined nonlinearities: the interaction Morawetz approach. https://doi.org/10.1137/23m1559063

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