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Recently low-regularity behaviour of solutions to cubic Dirac equations withthe Hartree-type nonlinearity has been extensively studied in somewhat aspecific assumption on the structure of the nonlinearity. The key approach ofprevious results was to exploit the null structure in the nonlinearity and thedecay of the Yukawa potential. In this paper, we aim to go beyond; weinvestigate the strong scattering property of cubic Dirac equations with quitea general class of the Hartree-type nonlinearity, which covers the Coulombpotential as well as the Yukawa potential, and the bilinear form, in which onecannot use the specific null structure. As a direct application, we also obtainthe scattering for the boson-star equations with the scaling-critical Sobolevdata.

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