PreprintCC BY 4.0arXiv
Pullback exponential attractors for 3D non-autonomous Boussinesq equations with fractional Laplacian
Abstract
Focusing on the pullback asymptotic behavior exhibited by the system, this paper studies the three-dimensional (3D) non-autonomous Boussinesq equations with fractional Laplacian. For $ α> \frac{5}{4} $ and $ β> \frac{5}{8} $, by adopting the $ \ell $-trajectory method introduced in \cite{MP2002}, we demonstrate the existence of both a finite-dimensional pullback attractor and a pullback exponential attractor for the process $ \{L(t, τ)\}_{t \geq τ} $ that corresponds to \cref{eq0101} in the phase space $ X_{\ell} $. Furthermore, we establish the existence of a pullback exponential attractor for the process $ \{U(t, τ)\}_{t \geq τ} $ within the original phase space $ H_σ^α(Ω) \times H^β(Ω) $.
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BibTeX
@misc{kou2026pullback,
title = {{Pullback exponential attractors for 3D non-autonomous Boussinesq equations with fractional Laplacian}},
author = {Tong Kou and Hui Liu and Xiuqing Wang and Jie Xin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18114},
eprint = {2609.18114},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18114},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pullback exponential attractors for 3D non-autonomous Boussinesq equations with fractional Laplacian
AU - Tong Kou
AU - Hui Liu
AU - Xiuqing Wang
AU - Jie Xin
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18114
UR - https://arxiv.org/abs/2609.18114
AB - Focusing on the pullback asymptotic behavior exhibited by the system, this paper studies the three-dimensional (3D) non-autonomous Boussinesq equations with fractional Laplacian. For $ α> \frac{5}{4} $ and $ β> \frac{5}{8} $, by adopting the $ \ell $-trajectory method introduced in \cite{MP2002}, we demonstrate the existence of both a finite-dimensional pullback attractor and a pullback exponential attractor for the process $ \{L(t, τ)\}_{t \geq τ} $ that corresponds to \cref{eq0101} in the phase space $ X_{\ell} $. Furthermore, we establish the existence of a pullback exponential attractor for the process $ \{U(t, τ)\}_{t \geq τ} $ within the original phase space $ H_σ^α(Ω) \times H^β(Ω) $.
ER -