2021/01/23 by Kazuki Aoki, Aoki, Kazuki, Takahisa Inui +7
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2101.09423
openalex publication_date 2021/01/23 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
We consider the final state problem for the inhomogeneous nonlinear Schrödinger equation with a critical long-range nonlinearity. Given a prescribed asymptotic profile, which has a logarithmic phase correction compared with the free evolution, we construct a unique global solution which converges to the profile. As a consequence, the existence of modified wave operators for localized small scattering data is obtained. We also study the same problem for the case with the critical inverse-square potential under the radial symmetry. In particular, we construct the modified wave operators for the long-range nonlinear Schrödinger equation with the critical inverse-square potential in three space dimensions, under the radial symmetry.