Non-autonomous 2D Newton-Boussinesq equation with oscillating external forces and its uniform attractor

Xueli Song; Jianhua Wu

doi:10.3934/eect.2020102

Article Contents

2022, Volume 11, Issue 1: 41-65. Doi: 10.3934/eect.2020102

This issue Previous Article Lifespan of solutions to a damped plate equation with logarithmic nonlinearity Next Article Approximate controllability of second order impulsive systems with state-dependent delay in Banach spaces

Non-autonomous 2D Newton-Boussinesq equation with oscillating external forces and its uniform attractor

Xueli Song^1,2, and
Jianhua Wu^1, ,

1.
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710062, China
2.
College of Science, Xi'an University of Science and Technology, Xi'an, 710054, China

^* Corresponding author: Jianhua Wu
^* Corresponding author: Jianhua Wu

Received: January 1, 2020

Revised: August 1, 2020

Early access: November 2, 2020

Published online: February 1, 2022

The first author is supported in part by National Natural Science Foundation of China (Nos. 11601417), Natural Science Basic Research Plan in Shaanxi Province of China (Nos. 2018JM1047, 2019JM-283) and Postdoctoral Fund in Shaanxi Province of China (No. 2016BSHEDZZ112). The second author was supported by the National Natural Science Foundation of China (No. 11771262).

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Abstract

We consider a non-autonomous two-dimensional Newton-Boussinesq equation with singularly oscillating external forces depending on a small parameter $ \varepsilon $. We prove the existence of the uniform attractor $ A^\varepsilon $ when the Prandtl number $ P_r>1 $. Furthermore, under suitable translation-compactness and divergence type condition assumptions on the external forces, we obtain the uniform (with respect to $ \varepsilon $) boundedness of the related uniform attractors $ A^\varepsilon $ as well as the convergence of the attractor $ A^\varepsilon $ to the attractor $ A^0 $ as $ \varepsilon\rightarrow 0^+ $.

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Mathematics Subject Classification: Primary: 35B41, 35B40; Secondary: 35Q35.

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