Transference of bilinear restriction estimates to quadratic variation norms and the Dirac–Klein–Gordon system
Transference of bilinear restriction estimates to quadratic variation norms and the Dirac–Klein–Gordon system
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 …