Virial identity and dispersive estimates for the $n$-dimensional Dirac equation
Federico Cacciafesta
TL;DR
This paper generalizes a virial identity for the magnetic Dirac equation to any dimension and uses it to derive smoothing and Strichartz estimates for the perturbed equation.
Contribution
It extends the virial identity to all dimensions and applies it to obtain dispersive estimates for the magnetic Dirac equation.
Findings
Derived smoothing estimates for the n-dimensional Dirac equation.
Established Strichartz estimates for the perturbed Dirac equation.
Extended virial identity to general dimensions.
Abstract
We extend to general dimension the virial identity proved by Boussaid-D'Ancona-Fanelli for the 3D magnetic Dirac equation. As an application we deduce smoothing and Strichartz estimates for an -dimensional Dirac equation perturbed with a magnetic potential.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Mathematical Analysis and Transform Methods · Spectral Theory in Mathematical Physics