Cubic nonlinear Schrodinger equation on three dimensional balls with radial data

2006/08/28 by Ramona Anton, Anton, Ramona
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.math/0608689

openalex publication_date 2006/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove wellposedness of the Cauchy problem for the cubic nonlinear Schrodinger equation with Dirichlet boundary conditions and radial data on 3D balls. The main argument is based on a bilinear eigenfunction estimate and the use of X^s,b spaces. The last part presents a first attempt to study the non radial case. We prove bilinear estimates for the linear Schrodinger flow with particular initial data.

Citations

• Bilinear eigenfunction estimates and the nonlinear Schr�dinger equation on surfaces

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