Research Paper#Nonlinear Schrödinger Equation (NLS), Mathematical Physics🔬 ResearchAnalyzed: Jan 3, 2026 16:20
Blowup Rate for Rotational NLS with Repulsive Potential
Published:Dec 28, 2025 07:25
•1 min read
•ArXiv
Analysis
This paper provides an analytical proof of the blowup rate for the mass-critical nonlinear Schrödinger equation (NLS) with rotation and a repulsive harmonic potential. It uses a virial identity and a pseudo-conformal transform. The findings are significant because they reveal how the repulsive potential can lead to global solutions in the focusing RNLS, a phenomenon previously observed in the non-rotational case. Numerical simulations support the analytical results.
Key Takeaways
- •Provides an analytical proof of the blowup rate for a specific type of NLS equation.
- •Uses a virial identity and a pseudo-conformal transform in the proof.
- •Demonstrates that increasing the repulsive potential can lead to global solutions.
- •Includes numerical simulations to support the analytical findings.
Reference
“The paper proves the "log-log" blowup rate and describes the mass concentration behavior near the blowup time. It also finds that increasing the repulsive potential can lead to global solutions.”