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Scattering and blowup beyond the mass-energy threshold for the cubic NLS with a potential

Volume 172 / 2023

Ying Wang Colloquium Mathematicum 172 (2023), 143-163 MSC: Primary 35P25; Secondary 35Q55. DOI: 10.4064/cm8978-10-2022 Published online: 7 December 2022


We consider the focusing cubic nonlinear Schrödinger equation with a potential, $i \partial _{t}u+(\Delta -V)u+|u|^{2}u=0$, with finite energy and finite variance initial data in dimension $3$. We investigate the scattering versus blow up dichotomy above the mass-energy threshold for finite variance solutions. Key ingredients in the proof include variational analysis, a virial argument and the concentration-compactness/rigidity method.


  • Ying WangGraduate School of China Academy of Engineering Physics
    Beijing, China, 100088

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