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Friday, October 25, 2019
3:00 PM - 4:00 PM
Linde Hall 255

Analysis Seminar

Sharp well-posedness for some integrable PDEs
Benjamin Harrop-Griffiths, Department of Mathematics, UCLA,

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.

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