Higher-Order Heat Estimates and Semilinear Heat Equations on the Noncommutative Torus
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917530865500160 |
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| author | Yang, Fulin Yang, Zhipeng |
| author_facet | Yang, Fulin Yang, Zhipeng |
| contents | We establish sharp higher-order heat estimates with complete bound on the noncommutative tori \(\mathbb{T}_θ^{n}\) and show the optimality in the small-time order. As an application in polynomial semilinear heat equations on \(\mathbb{T}_θ^{n}\), we give local well-posedness, the blow-up alternative, persistence of higher regularity, and instantaneous smoothing in the Sobolev algebra scale \(H^k_θ\), \(k>n/2\). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25513 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Higher-Order Heat Estimates and Semilinear Heat Equations on the Noncommutative Torus Yang, Fulin Yang, Zhipeng Analysis of PDEs Functional Analysis 46L52, 42B15, 35K58 We establish sharp higher-order heat estimates with complete bound on the noncommutative tori \(\mathbb{T}_θ^{n}\) and show the optimality in the small-time order. As an application in polynomial semilinear heat equations on \(\mathbb{T}_θ^{n}\), we give local well-posedness, the blow-up alternative, persistence of higher regularity, and instantaneous smoothing in the Sobolev algebra scale \(H^k_θ\), \(k>n/2\). |
| title | Higher-Order Heat Estimates and Semilinear Heat Equations on the Noncommutative Torus |
| topic | Analysis of PDEs Functional Analysis 46L52, 42B15, 35K58 |
| url | https://arxiv.org/abs/2605.25513 |