Two minimization problems on non-scattering solutions to mass-subcritical nonlinear Schrödinger equation

2016/05/30 by Satoshi Masaki, Masaki, Satoshi · 11 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Applied mathematics #FOS: Mathematics #Mathematical analysis #Mathematical optimization #Mathematics #Minification #Nonlinear Schrödinger equation #Nonlinear Waves and Solitons #Nonlinear system #Physics #Quantum mechanics #Scattering #Schrödinger equation #Spectral Theory in Mathematical Physics #math.AP

paper · pdf · doi:10.48550/arxiv.1605.09234

published in arXiv (Cornell University) (Cornell University) · 47 pages

arxiv created 2016/05/30 · openalex publication_date 2016/05/30 · arxiv updated 2016/05/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce two minimization problems on non-scattering solutions to nonlinear Schrödinger equation. One gives us a sharp scattering criterion, the other is concerned with minimal size of blowup profiles. We first reformulate several previous results in terms of these two minimizations. Then, the main result of the paper is existence of minimizers to the both minimization problems for mass-subcritical nonlinear Schrödinger equations. To consider the latter minimization, we consider the equation in a Fourier transform of generalized Morrey space. It turns out that the minimizer to the latter problem possesses a compactness property, which is so-called almost periodicity modulo symmetry.

Citations

• Global well - posedness and scattering for the focusing, energy - critical nonlinear Schrödinger problem in dimension d = 4 for initial data below a ground state threshold
• On minimal non-scattering solution for focusing mass-subcritical nonlinear Schrödinger equation
• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• A Sharp Condition for Scattering of the Radial 3D Cubic Nonlinear Schrödinger Equation
• A sharp scattering condition for focusing mass-subcritical nonlinear Schrödinger equation

Cited by

• Characterization of Vanishing Campanato Spaces via Ball Banach Function Spaces and Its Applications
• The preduals of Banach space valued Bourgain-Morrey spaces

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