Global well-posedness of the energy-critical complex Ginzburg-Landau equation in exterior domains
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909993652977664 |
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| author | Cheng, Xing Guo, Chang-Yu Zheng, Jiqiang Zheng, Yunrui |
| author_facet | Cheng, Xing Guo, Chang-Yu Zheng, Jiqiang Zheng, Yunrui |
| contents | In this article, we consider an energy-critical complex Ginzburg-Landau equation in the exterior of a smooth compact strictly convex obstacle. We prove the global well-posedness of energy-critical complex Ginzburg-Landau equation in an exterior domain by the concentration-compactness/rigidity theorem method. As corollaries of our main result, we establish both the existence of global weak solutions to energy-critical defocusing nonlinear Schrödinger equations and the global well-posedness theory for energy-critical semi-linear heat equation in exterior domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04381 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of the energy-critical complex Ginzburg-Landau equation in exterior domains Cheng, Xing Guo, Chang-Yu Zheng, Jiqiang Zheng, Yunrui Analysis of PDEs In this article, we consider an energy-critical complex Ginzburg-Landau equation in the exterior of a smooth compact strictly convex obstacle. We prove the global well-posedness of energy-critical complex Ginzburg-Landau equation in an exterior domain by the concentration-compactness/rigidity theorem method. As corollaries of our main result, we establish both the existence of global weak solutions to energy-critical defocusing nonlinear Schrödinger equations and the global well-posedness theory for energy-critical semi-linear heat equation in exterior domains. |
| title | Global well-posedness of the energy-critical complex Ginzburg-Landau equation in exterior domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.04381 |