A new class of critical solutions for 1D cubic NLS

2022/12/16 by Anatole Guérin, Guérin, Anatole
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2212.08564

openalex publication_date 2022/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this article is to prove the existence of a new class of solutions of 1D cubic NLS with an initial data related to a sum of Dirac masses, of critical regularity F(L^∞), and belonging to H^s for any s <-1/2. This problem is motivated by the lack of result for critical regularity initial condition. Our result is based on a scattering approach, after performing a pseudo-conformal transformation, and on fine estimations of oscillatory integrals.

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