2016/05/31 by Timothy Candy, Sebastian Herr · 28 citations
Mathematics · Medicine · #Advanced Mathematical Physics Problems #Bilinear interpolation #Bounded function #Dirac (video compression format) #Fourier transform #Geometry #Invariant (physics) #Klein–Gordon equation #Mathematical analysis #Mathematical physics #Mathematics #Navier-Stokes equation solutions #Nonlinear system #Physics #Pure mathematics #Quadratic equation #Quantum mechanics #Sobolev space #Soft tissue tumor case studies #math.AP #math.CA
paper · pdf · doi:10.2140/apde.2018.11.1171
published in Analysis & PDE 11(5), 1171-1240 (Mathematical Sciences Publishers) · v2: minor typos fixed, few references added, case 2M=m included; v3: minor edits, v4: assumptions rephrased, minor corrections/additions
arxiv created 2017/04/03 · openalex publication_date 2018/04/11 · arxiv updated 2018/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.