The limit theory of the energy-critical complex Ginzburg-Landau equation

2023/11/01 by Xing Cheng, Cheng, Xing., Guo, Chang-yu +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2311.00499

openalex publication_date 2023/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the limit behavior of the solutions to energy-critical complex Ginzburg-Landau equation. We give a rigorous theory of the zero-dispersion limit from energy-critical complex Ginzburg-Landau equation to energy-critical nonlinear heat equation for dimensions 3 and 4 in both the defocusing and focusing cases by energy method. Furthermore, we also show the invisicid limit of energy-critical complex Ginzburg-Landau equation to energy-critical nonlinear Schrödinger equation for dimension 4 in the focusing case.

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