Going Beyond the Threshold: Scattering and Blow-up in the Focusing NLS Equation
Article
Duyckaerts, T, Roudenko, S. (2015). Going Beyond the Threshold: Scattering and Blow-up in the Focusing NLS Equation
. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 334(3), 1573-1615. 10.1007/s00220-014-2202-y
Duyckaerts, T, Roudenko, S. (2015). Going Beyond the Threshold: Scattering and Blow-up in the Focusing NLS Equation
. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 334(3), 1573-1615. 10.1007/s00220-014-2202-y
We study the focusing nonlinear Schrödinger equation (Formula presented.) in the L2-supercritical regime with finite energy and finite variance initial data. We investigate solutions above the energy (or mass–energy) threshold. In our first result, we extend the known scattering versus blow-up dichotomy above the mass–energy threshold for finite variance solutions in the energy-subcritical and energy-critical regimes, obtaining scattering and blow-up criteria for solutions with arbitrary large mass and energy. As a consequence, we characterize the behavior of the ground state initial data modulated by a quadratic phase. Our second result gives two blow up criteria, which are also applicable in the energy-supercritical NLS setting. We finish with various examples illustrating our results.
