The limit theory of the energy-critical complex Ginzburg-Landau equation
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929324252200960 |
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| author | Cheng, Xing. Guo, Chang-yu Zheng, Yunrui. |
| author_facet | Cheng, Xing. Guo, Chang-yu Zheng, Yunrui. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00499 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The limit theory of the energy-critical complex Ginzburg-Landau equation Cheng, Xing. Guo, Chang-yu Zheng, Yunrui. Analysis of PDEs 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. |
| title | The limit theory of the energy-critical complex Ginzburg-Landau equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2311.00499 |