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arXiv · 2311.00499

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

Xing. Cheng·Chang-yu Guo·Yunrui. Zheng
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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 Schr\"odinger equation for dimension 4 in the focusing case.

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Xing. Cheng, Chang-yu Guo, Yunrui. Zheng. 2023-11-01. The limit theory of the energy-critical complex Ginzburg-Landau equation. https://arxiv.org/abs/2311.00499

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