The cubic Dirac equation: Small initial data in $H^{\frac{1}{2}}({\mathbb{R}}^2)$

Abstract

Global well-posedness and scattering for the cubic Dirac equation with small initial data in the critical space $H^{\frac{1}{2}}({\mathbb{R}}^2)$ 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.

58 pages. Notation, setup and general reductions are adopted from our work arXiv:1310.5280, where we address the same problem in the 3d case. The analysis is significantly different. v3: 56 pages, Correction of the definitions of the sets Λ_{k,ω} and Λ_{k,ω}^{j}

References in corpus (2)

• Global well-posedness for the massless cubic Dirac equation
• A counterexample to an endpoint bilinear Strichartz inequality

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