English

Scattering below the ground state for the intercritical non-radial inhomogeneous NLS

Analysis of PDEs 2023-02-07 v1

Abstract

We consider the focusing inhomogeneous nonlinear Schr\"odinger equation itu+Δu+xbuαu=0onR×RN, i\partial_t u + \Delta u + |x|^{-b}|u|^\alpha u = 0\quad\text{on}\quad\mathbb{R}\times\mathbb{R}^N, with N2N\geq 2, 0<b<min{N2,2}0<b<\min\{\tfrac{N}{2},2\}, and 42bN<α<42bN2\tfrac{4-2b}{N}<\alpha<\tfrac{4-2b}{N-2}. These constraints make the equation mass-supercritical and energy-subcritical. We extend the results of Farah-Guzm\'an and Miao-Murphy-Zheng and prove scattering below the ground state with general initial data.

Keywords

Cite

@article{arxiv.2007.06165,
  title  = {Scattering below the ground state for the intercritical non-radial inhomogeneous NLS},
  author = {Mykael Cardoso and Luiz Gustavo Farah and Carlos M. Guzmán and Jason Murphy},
  journal= {arXiv preprint arXiv:2007.06165},
  year   = {2023}
}

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20 pages