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arXiv · 2604.21226

Smoothness of Inertial Manifold for the Burgers Equation

Ziqi Niu·Xinhua Li·Chunyou Sun·Xiaoqing Yang
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Abstract

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.

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Ziqi Niu, Xinhua Li, Chunyou Sun, Xiaoqing Yang. 2026-04-23. Smoothness of Inertial Manifold for the Burgers Equation. https://arxiv.org/abs/2604.21226

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