Abstract
We study the asymptotic dynamics for solutions to a system of nonlinear Schrödinger equations with cubic interactions, arising in nonlinear optics. We provide sharp threshold criteria leading to global well-posedness and scattering of solutions, as well as formation of singularities in finite time for (anisotropic) symmetric initial data. The free asymptotic results are proved by means of Morawetz and interaction Morawetz estimates. The blow-up results are shown by combining variational analysis and an ODE argument, which overcomes the unavailability of the convexity argument based on virial-type identities.
Original language | English |
---|---|
Pages (from-to) | 2134-2170 |
Number of pages | 37 |
Journal | Communications in Partial Differential Equations |
Volume | 46 |
Issue number | 11 |
Early online date | 15 Jun 2021 |
DOIs | |
Publication status | Published - 2021 |
Keywords
- Blow-up
- cubic-type interactions
- Morawetz estimates
- nonlinear Schrödinger systems
- scattering
ASJC Scopus subject areas
- Analysis
- Applied Mathematics