Firstly, bilinear Fourier restriction estimates — which are well known for free waves — are
extended to adapted spaces of functions of bounded quadratic variation, under quantitative
assumptions on the phase functions. This has applications to nonlinear dispersive equations,
in particular in the presence of resonances. Secondly, critical global well-posedness
and scattering results for massive Dirac–Klein–Gordon systems in dimension three are
obtained, in resonant as well as in nonresonant regimes. The results apply to small initial
data in scale-invariant Sobolev spaces exhibiting a small amount of angular regularity.
Keywords
bilinear Fourier restriction, adapted function spaces,
quadratic variation, atomic space, Dirac–Klein–Gordon
system, resonance, global well-posedness, scattering
