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October 1, 2018


Monday, October 01, 2018

(Cancelled) Seminars in Research in Biochemistry and Molecular Biology
12:00 PM - 1:00 PM

Bloomberg School of Public Health

Seminars in Research in Biochemistry and Molecular Biology
Aynur Bulut "TBA"
4:00 PM - 5:00 PM


Speaker: Aynur Bulut, (LSU) Title: "Logarithmically energy-supercritical Nonlinear Wave Equations: axial symmetry and global well-posedness." Abstract: In nonlinear dispersive PDE, radial symmetry often plays a key role in allowing for more refined analysis of the nonlinear interactions which could lead to possible blowup. We will describe recent work where we have recently introduced a mechanism for relaxing assumptions of radiality by considering symmetry in a subset of the variables (for instance, assuming that the initial data is axially symmetric). We applied this philosophy to show global well-posedness and scattering in for the nonlinear wave equation in the logarithmically energy-supercritical setting, generalizing a result of Tao which was established for the radial case. The uses Morawetz and Strichartz estimates that have been adapted to the new symmetry assumption. These methods in fact bring a new perspective to sharp estimates for the energy-critical problem, along the lines of the influential work of Ginibre, Soffer, and Velo. This is joint work with Ben Dodson.

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