Smoothness of Inertial Manifold for the Burgers Equation
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914500917067776 |
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| author | Niu, Ziqi Li, Xinhua Sun, Chunyou Yang, Xiaoqing |
| author_facet | Niu, Ziqi Li, Xinhua Sun, Chunyou Yang, Xiaoqing |
| contents | This paper establishes a ${C^{n,\varepsilon }}$-smooth extension of the inertial manifold for the one-dimensional Burgers equation, which demonstrates that its long-time behavior can be completely determined by explicit smooth first-order ODEs. We first devise a new framework for an abstract equation with two nonlinear terms, where one preserves regularity and the other reduces regularity, and derive sufficient conditions for constructing the ${C^{n,\varepsilon}}$-smooth extension of the IM by treating these two nonlinear terms separately. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21226 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Smoothness of Inertial Manifold for the Burgers Equation Niu, Ziqi Li, Xinhua Sun, Chunyou Yang, Xiaoqing Dynamical Systems This paper establishes a ${C^{n,\varepsilon }}$-smooth extension of the inertial manifold for the one-dimensional Burgers equation, which demonstrates that its long-time behavior can be completely determined by explicit smooth first-order ODEs. We first devise a new framework for an abstract equation with two nonlinear terms, where one preserves regularity and the other reduces regularity, and derive sufficient conditions for constructing the ${C^{n,\varepsilon}}$-smooth extension of the IM by treating these two nonlinear terms separately. |
| title | Smoothness of Inertial Manifold for the Burgers Equation |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2604.21226 |