The Cubic Dirac Equation: Small Initial Data in H-1/2 (R-2)
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The Cubic Dirac Equation: Small Initial Data in H-1/2 (R-2)

  • Author(s): Bejenaru, Ioan
  • Herr, Sebastian
  • et al.
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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