Sharp decay estimates for critical Dirac equations

TL;DR

This paper establishes precise decay estimates for critical Dirac equations in multiple contexts, including on manifolds and honeycomb structures, and classifies solutions like ground and excited states.

Contribution

It provides the first sharp pointwise decay estimates for critical Dirac equations and explicitly characterizes excited states and solution classifications.

Findings

Sharp decay estimates for solutions on -dimensional space.

Explicit asymptotic behavior for excited states.

Classification results for ground and excited states.

Abstract

We prove sharp pointwise decay estimates for critical Dirac equations on $\mathbb{R}^n$ with $n\geq 2$. They appear for instance in the study of critical Dirac equations on compact spin manifolds, describing blow-up profiles, and as effective equations in honeycomb structures. For the latter case, we find excited states with an explicit asymptotic behavior. Moreover, we provide some classification results both for ground states and for excited states.