Low regularity solutions for the general quasilinear ultrahyperbolic Schrödinger equation
Metadata only
Date
2023-12Type
- Report
ETH Bibliography
yes
Altmetrics
Abstract
We present a novel method for establishing large data local well-posedness in low regularity Sobolev spaces for general quasilinear Schrödinger equations with non-degenerate and nontrapping metrics. Our result represents a definitive 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 by 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. Show more
Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
Quasilinear Schrödinger; Ultrahyperbolic; Local well-posednessOrganisational unit
09603 - Alaifari, Rima / Alaifari, Rima
More
Show all metadata
ETH Bibliography
yes
Altmetrics