Blow-up and scattering in the focusing dispersive equations.
Connections for Women: Dispersive and Stochastic PDE August 19, 2015 - August 21, 2015
Location: MSRI: Simons Auditorium
invariant solution set
ground state energy estimate
35Q55 - NLS-like equations (nonlinear Schrödinger) [See also 37K10]
35Qxx - Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05]
35P30 - Nonlinear eigenvalue problems, nonlinear spectral theory
We study the focusing nonlinear Schrodinger equation with finite energy and finite variance initial data. While considering the mass-supercritical regime we investigate solutions above the energy (or mass-energy) threshold, i.e., when the nergy of the solution exceeds the energy of the so-called ground state. We extend the known scattering versus blow-up dichotomy above the energy threshold for finite variance solutions in the energy-subcritical and energy-critical regimes, characterizing invariant sets of solutions (with either scattering or blow-up in finite time behavior) possibly with arbitrary large mass and energy. We investigate other dispersive equations in a similar manner.
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