2018/07/05 by Timothy Candy, Sebastian Herr · 14 citations
Mathematics · #Advanced Mathematical Physics Problems #Algebra over a field #Arithmetic #Bilinear interpolation #Computer science #Dimension (graph theory) #Division (mathematics) #Fourier transform #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematics #Modular design #Navier-Stokes equation solutions #Pure mathematics #Space (punctuation) #math.AP
paper · pdf · doi:10.1007/s40818-018-0054-z
published in Annals of PDE 4(2) (Springer Science+Business Media) · Section 7 contains a proof of a special case of the bilinear estimate obtained in 1707.08944
arxiv created 2018/07/05 · openalex publication_date 2018/12/01 · arxiv updated 2018/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider Wave Maps into the sphere and give a new proof of small data global well-posedness and scattering in the critical Besov space, in any space dimension n ≥ 2. We use an adapted version of the atomic space U2 as the single building block for the iteration space. Our approach to the so-called division problem is modular as it systematically uses two ingredients: atomic bilinear (adjoint) Fourier restriction estimates and an algebra property of the iteration space, both of which can be adapted to other phase functions.