Scattering of cubic Dirac equations with a general class of Hartree-type nonlinearity for the critical Sobolev data

TL;DR

This paper proves strong scattering results for cubic Dirac equations with a broad class of Hartree-type nonlinearities, including Coulomb and Yukawa potentials, extending previous results that relied on specific null structures.

Contribution

It advances the understanding of scattering for cubic Dirac equations by handling more general Hartree-type nonlinearities without relying on null structure.

Findings

Established scattering for cubic Dirac equations with general Hartree nonlinearities.

Extended results to include Coulomb and Yukawa potentials.

Applied findings to boson-star equations with critical Sobolev data.

Abstract

Recently low-regularity behaviour of solutions to cubic Dirac equations with the Hartree-type nonlinearity has been extensively studied in somewhat a specific assumption on the structure of the nonlinearity. The key approach of previous results was to exploit the null structure in the nonlinearity and the decay of the Yukawa potential. In this paper, we aim to go beyond; we investigate the strong scattering property of cubic Dirac equations with quite a general class of the Hartree-type nonlinearity, which covers the Coulomb potential as well as the Yukawa potential, and the bilinear form, in which one cannot use the specific null structure. As a direct application, we also obtain the scattering for the boson-star equations with the scaling-critical Sobolev data.