Energy Critical NLS in two space dimensions

2008/06/18 by Jim Colliander, Colliander, Jim, Slim Ibrahim +5
Mathematics · Medicine · Physics and Astronomy · #35-xx #35B33 #35B60 #35Q55 #37K07 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Polyomavirus and related diseases

paper · pdf · doi:10.48550/arxiv.0806.2979

openalex publication_date 2008/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the initial value problem for a defocusing nonlinear Schrödingerequation with exponential nonlinearity. We identify subcritical, critical and supercritical regimes in the energy space. We establish global well-posedness in the subcritical and critical regimes. Well-posedness fails to hold in the supercritical case.

Citations

• Trudinger type inequalities in 𝐑^𝐍 and their best exponents

Related

• Energy critical Schrödinger equation with weighted exponential nonlinearity I: Local and global well-posedness
• Numerical simulations of the energy- supercritical Nonlinear Schrödinger equation
• The energy-critical NLS with inverse-square potential
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• The defocusing energy-supercritical inhomogeneous NLS in four space dimension