Nonlinear Partial Differential Equations

Date: March 29, 2022

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Benjamin Harrop-Griffiths, UCLA

Title: The derivative NLS on the line

Abstract: The derivative nonlinear Schrödinger equation arises as an effective equation for the dynamics of Alfvén waves in plasmas. While this model has been analyzed in depth since the 1970s, the last two years have seen a significant amount of progress on the behavior of solutions in Sobolev spaces. In this talk we discuss some of these recent results and present a proof of well-posedness for all initial data on the line with finite mass. This is joint work with Rowan Killip, Maria Ntekoume, and Monica Vişan.