Electron. J. Differential Equations, Vol. 2019 (2019), No. 80, pp. 1-18.

Dynamics of 2D Navier-Stokes equations with Rayleigh's friction and distributed delay

Yadi Wang, Xin-Guang Yang, Xingjie Yan

This article concerns the long time dynamics of a 2D incompressible Navier-Stokes equation with Rayleigh's friction and distributed delay. Under appropriate assumptions on the external force and delay term, we obtain global well-posedness in new phase spaces with delay. Using uniform estimates and compact embedding, we obtain a global attractor.

Submitted June 21, 2018. Published June 12, 2019.
Math Subject Classifications: 35Q30, 35B40, 35B41, 76D03, 76D05.
Key Words: Navier-Stokes equations; distributed delay; Rayleigh's friction.

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Yadi Wang
School of Computer Science and Engineering
Southeast University
Ningjing, 211189, China
email: yadiwang@seu.edu.cn
Xin-Guang Yang
Department of Mathematics and Information Science
Henan Normal University
Xinxiang, 453007, China
email: yangxinguang@hotmail.com
Xingjie Yan
College of Science
China University of Mining and Technology
Xuzhou, 221008, China
email: yanxj04@163.com

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