Analysis Seminar

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Low regularity solutions for the general quasilinear ultrahyperbolic Schrodinger equation

Speaker: Benjamin Pineau, New York University

Location: Warren Weaver Hall 1302

Date: Thursday, September 19, 2024, 11 a.m.

Synopsis:

I will present a novel method for establishing large data local well-posedness in low regularity
Sobolev spaces for general quasilinear Schr ̈odinger equations with non-degenerate and nontrapping metrics.
Our result represents a substantial improvement over the landmark results of Kenig, Ponce, Rolvung and
Vega, as it weakens the regularity and decay assumptions to the same scale of spaces considered in a recent
paper of Marzuola, Metcalfe, and Tataru, but removes the uniform ellipticity assumption on the metric
from their result. Our method has the additional benefit of being relatively simple but also very robust. In
particular, it only relies on the use of pseudodifferential calculus for classical symbols. This is joint work
with Mitchell Taylor.