Dynamics of the stochastic velocity-vorticity-Voigt model of the 3D Navier-Stokes equations with damping and memory

Dang Thanh Son; Bui Kim My; Nguyen Duong Toan

doi:10.3934/dcdss.2025137

Article Contents

2026, Volume 19: 127-156. Doi: 10.3934/dcdss.2025137

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Dynamics of the stochastic velocity-vorticity-Voigt model of the 3D Navier-Stokes equations with damping and memory

1.
Foundation Sciences Faculty, Telecommunications University, 101 Mai Xuan Thuong, Bac Nha Trang, Khanh Hoa, Vietnam
2.
Faculty of Primary Education, Hanoi Pedagogical University 2, 32 Nguyen Van Linh, Xuan Hoa, Phu Tho, Vietnam
3.
Department of Mathematics, Haiphong University, 171 Phan Dang Luu, Phu Lien, Haiphong, Vietnam

^*Corresponding author: Bui Kim My
^*Corresponding author: Bui Kim My

Received: June 2025

Revised: September 2025

Early access: September 22, 2025

Published online: September 22, 2025

This research is funded by Vietnam Ministry of Education and Training under grant number B.2024-CTT-06, and Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2023.29.

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Abstract

In this paper, we study the asymptotic behavior of solutions of the non-autonomous stochastic velocity-vorticity-Voigt model of the 3D Navier-Stokes equations with damping and memory driven by multiplicative white noise. We first show the existence of pullback random attractors when the intensity of noise is sufficiently small. Then we show the upper semicontinuity of random attractors when the intensity of noise approaches zero. To the best of our knowledge, this is the first attempt to establish the existence as well as the upper semicontinuity of random attractors for the non-autonomous stochastic velocity-vorticity-Voigt model.

Keywords:

Random attractor,
upper semicontinuity,
stochastic velocity-vorticity-Voigt model,
damping,
memory.

Mathematics Subject Classification: Primary: 37L55, 37L30; Secondary: 35R60, 35B40, 35B41.

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