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Harmonic Analysis and Differential Equations Seminar

Event Type
Department of Mathematics
Altgeld Hall 143
May 7, 2024   1:00 pm  
Aynur Bulut (Louisiana State University)
Carrie Clark
Originating Calendar
Harmonic Analysis and Differential Equations Seminar (HADES)

Speaker: Aynur Bulut (Louisiana State University)

Title: New perspectives on scaling thresholds and quantitative criteria for blow-up

AbstractIn this talk, we give an overview of several recent results where quantitative estimates play a key role.  In the first part of the talk, we discuss new convex integration constructions for fluid systems with external forcing.  We will then discuss a novel application of these ideas to the surface quasi-geostrophic (SQG) equation.  Moving forward with the theme of quantitative estimates, in the second part of the talk we will describe new bounds for the defocusing energy-supercritical Nonlinear Schrödinger equation (NLS) and use these to give a universal blow-up criteria which goes below the scaling invariant threshold.  These results are in line with a recent breakthrough construction of finite-time blow-up solutions, and in particular give the first generic result distinguishing potential defocusing blow-up phenomena from many of the known examples of blow-up in the focusing setting. At the end of the talk, we will briefly describe applications to related models.

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