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

preprint2016arXivOpen access

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

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