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Non-autonomous 2D Newton-Boussinesq equation with oscillating external forces and its uniform attractor
Author(s) -
Xueli Song,
Jianhua Wu
Publication year - 2020
Publication title -
evolution equations and control theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 19
eISSN - 2163-2480
pISSN - 2163-2472
DOI - 10.3934/eect.2020102
Subject(s) - attractor , mathematics , combinatorics , physics , mathematical analysis
We consider a non-autonomous two-dimensional Newton-Boussinesq equation with singularly oscillating external forces depending on a small parameter \begin{document}$ \varepsilon $\end{document} . We prove the existence of the uniform attractor \begin{document}$ A^\varepsilon $\end{document} when the Prandtl number \begin{document}$ P_r>1 $\end{document} . Furthermore, under suitable translation-compactness and divergence type condition assumptions on the external forces, we obtain the uniform (with respect to \begin{document}$ \varepsilon $\end{document} ) boundedness of the related uniform attractors \begin{document}$ A^\varepsilon $\end{document} as well as the convergence of the attractor \begin{document}$ A^\varepsilon $\end{document} to the attractor \begin{document}$ A^0 $\end{document} as \begin{document}$ \varepsilon\rightarrow 0^+ $\end{document} .

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