Low regularity solutions to the logarithmic Schrodinger equation

2023/11/03 by Rémi Carles, Masayuki Hayashi, Carles, Rémi +3 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2311.01801

openalex publication_date 2023/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider the logarithmic Schrödinger equation, in various geometric settings. We show that the flow map can be uniquely extended from H¹ to L² , and that this extension is Lipschitz continuous. Moreover, we prove the regularity of the flow map in intermediate Sobolev spaces.

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• Small-time approximate controllability of the logarithmic Schr''dinger equation

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