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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

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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.

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