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arXiv · 1501.06874

The cubic Dirac equation: Small initial data in $H^{\frac12}(\mathbb{R}^2)$

Ioan Bejenaru·Sebastian Herr
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Abstract

Global well-posedness and scattering for the cubic Dirac equation with small initial data in the critical space $H^{\frac12}(\mathbb{R}^2)$ 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.

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Ioan Bejenaru, Sebastian Herr. 2016-03-30. The cubic Dirac equation: Small initial data in $H^{\frac12}(\mathbb{R}^2)$. https://doi.org/10.1007/s00220-015-2508-4

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