2015/01/31 by Ioan Bejenaru, Sebastian Herr · 67 citations
Mathematics · #Advanced Mathematical Physics Problems #Combinatorics #Computer science #Dimension (graph theory) #Dirac (video compression format) #Dirac equation #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Scattering #Space (punctuation) #math.AP #msc:35Q41
paper · pdf · doi:10.1007/s00220-015-2508-4
published in Communications in Mathematical Physics 343(2), 515-562 (Springer Science+Business Media) · 58 pages. Notation, setup and general reductions are adopted from our work arXiv:1310.5280, where we address the same problem in the 3d case. The analysis is significantly different. v3: 56 pages, Correction of the definitions of the sets Λ_{k,ω} and Λ_{k,ω}^{j}
openalex publication_date 2015/11/24 · arxiv created 2016/03/30 · arxiv updated 2016/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Global well-posedness and scattering for the cubic Dirac equation with small initial data in the critical space H\frac12(ℝ2) is established. The proof is based on a sharp endpoint Strichartz estimate for the Klein-Gordon equation in dimension n=2, which is captured by constructing an adapted systems of coordinate frames.