Friday, October 25, 2019

3:00 PM -
4:00 PM

Linde Hall 255

# Analysis Seminar

Series: Analysis Seminar Series

Sharp well-posedness for some integrable PDEs

Despite its innocuous appearance, the 1d cubic NLS is a truly remarkable PDE. Not only does it arise as a model in numerous physical scenarios, for example fluid dynamics and nonlinear optics, but it is also part of the select group of integrable equations, in the sense that it possesses a Lax pair and infinitely many conserved quantities. Building on the work of Killip and Visan on the KdV equation, in this talk we present a proof of well-posedness for the cubic NLS that combines its deep mathematical structure with robust PDE techniques to obtain a sharp result in Sobolev spaces. We will also discuss the corresponding results for an intimately related equation, the mKdV. This is joint work with Rowan Killip and Monica Visan.

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For more information, please contact Math Department by phone at 626-395-4335 or by email at mathinfo@caltech.edu.