Type: Article
Publication Date: 2021-07-14
Citations: 7
DOI: https://doi.org/10.4171/jst/362
We investigate L^1\to L^\infty dispersive estimates for the massless two dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies the natural t^{-\frac{1}{2}} decay rate, which may be improved to t^{-\frac{1}{2} - \gamma} for any 0\leq \gamma<\frac{3}{2} at the cost of spatial weights. We classify the structure of threshold obstructions as being composed of a two dimensional space of p-wave resonances and a finite dimensional space of eigenfunctions at zero energy. We show that, in the presence of a threshold resonance, the Dirac evolution satisfies the natural decay rate except for a finite-rank piece. While in the case of a threshold eigenvalue only, the natural decay rate is preserved. In both cases we show that the decay rate may be improved at the cost of spatial weights.