2411.09034
Global attractor and robust exponential attractors for some classes of fourth-order nonlinear evolution equations
Beniamin Goldys, Agus L. Soenjaya, Thanh Tran
correctmedium confidence
- Category
- math.DS
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves a robust family of exponential attractors for the fourth‑order PDE (1.1) in d ≤ 2 with λ2 = 0 via an abstract continuous‑time theorem (Theorem A.4), verified by uniform smoothing and parameter‑continuity lemmas; the candidate constructs them by a discrete EFNT short‑trajectory scheme with H^{-1}→H^1 bootstrapping. Both obtain the same properties (uniform fractal dimension, uniform exponential attraction, Hölder continuity in ε), under the same smallness and coercivity assumptions. The methods differ in presentation but are logically consistent and compatible.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The paper proves robust exponential attractors for a broad fourth-order PDE class in d ≤ 2, offering new uniform-in-ε estimates and a clean application of an abstract robust-attractor theorem. The results are correct and valuable for LLBar/LLB and CH–AC models. Some technical steps are sketched; minor additions of intermediate details and explicit reminders of key assumptions would enhance clarity for readers.