Local well-posedness for quasilinear Schrödinger equations with rough data

Jason Metcalfe
University of North Carolina, Chapel Hill, USA
12th March 2014 14:05-14:55, Carslaw Room 829 (AGR)
[Joint with Applied Mathematics Seminar]

Abstract

We will discuss recent joint works with J. Marzuola and D. Tataru that focus on local existence for generic quasilinear Schrodinger equations with data in low regularity spaces. The Mizohata integrability conditions plays an essential role in choosing appropriate spaces, and in order to incorporate the necessary decay, we choose Sobolev spaces that are adapted to include a summability over a partition of space into cubes. The primary estimate is a local smoothing estimate, which is adapted to these spaces.

Check also the PDE Seminar page. Enquiries to Daniel Hauer or Daniel Daners.