Global well-posedness of NLS with a rough potential below the energy norm

2013/01/03 by Younghun Hong, Hong, Younghun
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1301.0428

openalex publication_date 2013/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that in the presence of a rough external potential, a 3d cubic defocusing NLS is globally well-posed in H^s for s>5/6. The proof is based on the approach of Colliander-Keel-Staffilani-Takaoka-Tao, called the I-method, but in order to deal with a rough potential, we modify harmonic analysis tools by spectral theory.

Citations

• Structure of wave operators in R³

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