Sharp threshold for global existence and blowup in the focusing nonlinear Schrödinger equation with inverse-square potential
Abstract
Abstract This paper examines the focusing nonlinear Schrödinger equation with an inverse-square potential in R N ( N ≥ 3 ) ${\mathbb{R}}^{N} \left(N\ge 3\right)$ , where the nonlinear exponent lies between the mass-critical and energy-subcritical regimes. A central approach of this work is the construction of novel cross-invariant manifolds to address the challenge of proving blow-up within the potential well theory. Utilizing these manifolds, we establish a sharp threshold for the global existence and finite-time blow-up of weak solutions.
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Nonlinear Partial Differential Equations
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Advances in Nonlinear Analysis
- Volume
- 15
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN