Self-similar blowup for mass supercritical Schrödinger equations

2025/09/20 by Roland Donninger, Donninger, Roland, Lorenz Lichtnecker +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2509.16600

openalex publication_date 2025/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the focusing nonlinear Schrödinger equation in three spatial dimensions with powers close to three and prove the existence of a self-similar solution. This generalizes a previous result on the cubic case and shows that self-similar blowup is stable under perturbations of the equation.

Citations

• Self-Similar Singular Solutions to the Nonlinear Schrödinger and the Complex Ginzburg-Landau Equations
• Self-similar blowup for the cubic Schrödinger equation
• Self-similar blow-up profiles for slightly supercritical nonlinear Schrödinger equations
• A solution to the focusing 3d NLS that blows up on a contracting sphere
• A class of solutions to the 3d cubic nonlinear Schroedinger equation\n that blow-up on a circle
• Stable self similar blow up dynamics for slightly L² supercritical NLS equations

Related

• Self-similar blowup for the cubic Schrödinger equation
• Self-similar blow-up profiles for slightly supercritical nonlinear Schrödinger equations
• A note on the existence of self-similar profiles of the hydrodynamic formulation of the focusing nonlinear Schrödinger equation
• Stable self similar blow up dynamics for slightly L² supercritical NLS equations
• Self-Similar Singular Solutions to the Nonlinear Schrödinger and the Complex Ginzburg-Landau Equations