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arXiv · 2007.06165

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

Mykael Cardoso·Luiz Gustavo Farah·Carlos M. Guzmán·Jason Murphy
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Abstract

We consider the focusing inhomogeneous nonlinear Schr\"odinger equation \[ i\partial_t u + \Delta u + |x|^{-b}|u|^\alpha u = 0\quad\text{on}\quad\mathbb{R}\times\mathbb{R}^N, \] with $N\geq 2$, $0<b<\min\{\tfrac{N}{2},2\}$, and $\tfrac{4-2b}{N}<\alpha<\tfrac{4-2b}{N-2}$. 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.

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Mykael Cardoso, Luiz Gustavo Farah, Carlos M. Guzmán, Jason Murphy. 2020-07-13. Scattering below the ground state for the intercritical non-radial inhomogeneous NLS. https://arxiv.org/abs/2007.06165

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