Almost Sure Scattering at Mass Regularity for Radial Schrödinger Equations

2020/11/12 by Mickaël Latocca, Latocca, Mickaël · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2011.06309

openalex publication_date 2020/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the radial nonlinear Schrödinger equation i∂_tu +Δu = |u|^p-1u in dimension d\geqslant 2 for p∈ (1,1+(4)/(d)] and construct a natural Gaussian measure μ₀ which support is almost L²_rad and such that μ₀ - almost every initial data gives rise to a unique global solution. Furthermore, for p>1+(2)/(d) and d∈\2, …, 10\ the solutions constructed scatters in a space which is almost L². This paper can be viewed as the higher dimensional counterpart of the work of Burq and Thomann, in the radial case.

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