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Peer-reviewedCC BYElectronic Journal of Differential Equations

Dynamics of weak solutions for two-dimensional micropolar equations with nonlinear damping

  • Xueli Song1
  • Xinyu Liu1
  1. 1Xi'an Univ. of Science and Technology, Xi'an, China
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Abstract

In this article, we consider 2D micropolar fluid equations with a nonlinear damping term σ|u|β−1u with 1 ≤ β < 7/3. We establish the existence and uniqueness of weak solutions. Based on the method of ℓ-trajectory proposed by Malek and Prazak, we analyze the long-time behavior of the system in the trajectory space Xℓ, deduce the existence of the global attractor of the semigroup in the initial phase space H× L2(Ω), and establish that this global attractor has finite fractal dimension.

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Cite

BibTeXRIS
BibTeX
@article{song2026dynamics,
  title = {{Dynamics of weak solutions for two-dimensional micropolar equations with nonlinear damping}},
  author = {Xueli Song and Xinyu Liu},
  journal = {Electronic Journal of Differential Equations},
  year = {2026},
  month = sep,
  url = {http://ejde.math.txstate.edu/Volumes/2026/70/abstr.html},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Dynamics of weak solutions for two-dimensional micropolar equations with nonlinear damping
AU  - Xueli Song
AU  - Xinyu Liu
PY  - 2026
DA  - 2026/09/01
JO  - Electronic Journal of Differential Equations
UR  - http://ejde.math.txstate.edu/Volumes/2026/70/abstr.html
AB  - In this article, we consider 2D micropolar fluid equations with a nonlinear damping term σ|u|^β−1u with 1 ≤ β < 7/3. We establish the existence and uniqueness of weak solutions. Based on the method of ℓ-trajectory proposed by Malek and Prazak, we analyze the long-time behavior of the system in the trajectory space X_ℓ, deduce the existence of the global attractor of the semigroup in the initial phase space H× L^2(Ω), and establish that this global attractor has finite fractal dimension.
SN  - 1072-6691
ER  -