School of Science
Xi'an University of Science and Technology
Xi'an 710054, China
email: songxlmath@163.com
School of Science
Xi'an University of Science and Technology
Xi'an 710054, China
email: 1220750649@qq.com
Xueli Song, Xinyu Liu
Abstract:
In this article, we consider 2D micropolar fluid equations with a nonlinear damping
term \(\sigma|u|^{\beta-1}u\) with \(1 \leq \beta < 7/3\). We establish the existence
and uniqueness of weak solutions. Based on the method of
\(\ell \)-trajectory proposed by Malek and
Prazak, we analyze the long-time behavior of the system in the
trajectory space \(X_\ell\), deduce the existence of the global attractor of the
semigroup in the initial phase space \(H\times L^2(\Omega)\), and
establish that this global attractor has finite fractal dimension.
Submitted April 10, 2026. Published September 14, 2026.
Math Subject Classifications: 35B40, 35B41, 35Q35.
Key Words: 2D micropolar equation; nonlinear damping term; global attractor; Lipschitz continuous; \(\ell\)-trajectory.
DOI: 10.58997/ejde.2026.70
Show me the PDF file (436 KB), TEX file for this article.
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Xueli Song School of Science Xi'an University of Science and Technology Xi'an 710054, China email: songxlmath@163.com |
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Xinyu Liu School of Science Xi'an University of Science and Technology Xi'an 710054, China email: 1220750649@qq.com |
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