Events for 11/10/2020 from all calendars

Nonlinear Partial Differential Equations

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Aynur Bulut, Louisiana State University

Title: Quantitative blow-up criteria for defocusing energy-supercritical NLS

Abstract: In this talk, we describe recent work on quantitative bounds for the defocusing Nonlinear Schrodinger equation in the energy-supercritical regime. In particular, inspired bya recent breakthrough construction of finite-time blow-up solutions for the defocusing equation, we establish a blow-up criteria below the scaling invariant threshold. This gives the first generic result distinguishing potential defocusing blow-up phenomena from many of the known examples of blow-up in the focusing setting. The main tools involved include delicate refinements of induction on scales arguments due to Bourgain and Tao, combined with an interpolation argument which allows to break the scaling threshold.