Global strong well-posedness of the CAO-problem introduced by Lions, Temam and Wang
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910950822510592 |
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| author | Binz, Tim Brandt, Felix Hieber, Matthias Zöchling, Tarek |
| author_facet | Binz, Tim Brandt, Felix Hieber, Matthias Zöchling, Tarek |
| contents | Consider the CAO-problem introduced by Lions, Temam and Wang, which concerns a system of two fluids described by two primitive equations coupled by fully nonlinear interface conditions. They proved in their pioneering work the existence of a weak solution to the CAO-system; its uniqueness remained an open problem. In this article, it is shown that this coupled CAO-system is globally strongly well-posed for large data, even in critical Besov spaces. It is furthermore shown that, away from the boundary, the solution is even real analytic. The approach presented relies on an optimal data result for the boundary terms in the linearized system in terms of time-space Triebel-Lizorkin spaces. Boundary terms are then controlled by paraproduct methods in these spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11952 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global strong well-posedness of the CAO-problem introduced by Lions, Temam and Wang Binz, Tim Brandt, Felix Hieber, Matthias Zöchling, Tarek Analysis of PDEs 35Q86, 35Q35, 76D03, 35K55 Consider the CAO-problem introduced by Lions, Temam and Wang, which concerns a system of two fluids described by two primitive equations coupled by fully nonlinear interface conditions. They proved in their pioneering work the existence of a weak solution to the CAO-system; its uniqueness remained an open problem. In this article, it is shown that this coupled CAO-system is globally strongly well-posed for large data, even in critical Besov spaces. It is furthermore shown that, away from the boundary, the solution is even real analytic. The approach presented relies on an optimal data result for the boundary terms in the linearized system in terms of time-space Triebel-Lizorkin spaces. Boundary terms are then controlled by paraproduct methods in these spaces. |
| title | Global strong well-posedness of the CAO-problem introduced by Lions, Temam and Wang |
| topic | Analysis of PDEs 35Q86, 35Q35, 76D03, 35K55 |
| url | https://arxiv.org/abs/2505.11952 |