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The cubic Dirac equation in $H^\frac12(\R^2)$

New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems October 19, 2015 - October 30, 2015

October 30, 2015 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Ioan Bejenaru (University of California, San Diego)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • scattering results

  • global well-posedness

  • small data

  • massive vs massless

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14403

Abstract

Global well-posedness and scattering for the cubic Dirac equation with small initial data in the critical space $H^{\frac12}(\R^2)$ is established. The proof is based on a sharp endpoint Strichartz estimate for the Klein-Gordon equation in dimension $n=2$, which is captured by constructing an adapted systems of coordinate frames. This is joint work with S. Herr.

Supplements
24888?type=thumb Bejenaru-Notes 52.1 KB application/pdf Download
24889?type=thumb Bejenaru-Talk 679 KB application/pdf Download
Video/Audio Files

14403

H.264 Video 14403.mp4 249 MB video/mp4 rtsp://videos.msri.org/data/000/024/699/original/14403.mp4 Download
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