Abstract:We establish sharp higher-order heat estimates with complete bound on the noncommutative tori \(\mathbb{T}_{\theta}^{n}\) and show the optimality in the small-time order. As an application in polynomial semilinear heat equations on \(\mathbb{T}_{\theta}^{n}\), we give local well-posedness, the blow-up alternative, persistence of higher regularity, and instantaneous smoothing in the Sobolev algebra scale \(H^k_\theta\), \(k>n/2\).
| Comments: | 18 pages, comments are welcome |
| Subjects: | Analysis of PDEs (math.AP); Functional Analysis (math.FA) |
| MSC classes: | 46L52, 42B15, 35K58 |
| Cite as: | arXiv:2605.25513 [math.AP] |
| (or arXiv:2605.25513v1 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25513 arXiv-issued DOI via DataCite (pending registration) |
From: Zhipeng Yang [view email]
[v1]
Mon, 25 May 2026 07:17:26 UTC (15 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。