J. Korean Math. Soc. 2024; 61(2): 227-253
Online first article February 23, 2024 Printed March 1, 2024
https://doi.org/10.4134/JKMS.j220380
Copyright © The Korean Mathematical Society.
Cung The Anh, Vu Manh Toi, Phan Thi Tuyet
Hanoi National University of Education; Thuyloi University; Electric Power University
This paper studies the existence of weak solutions and the stability of stationary solutions to stochastic 3D globally modified Navier-Stokes equations with unbounded delays in the phase space $BCL_{-\infty}(H)$. We first prove the existence and uniqueness of weak solutions by using the classical technique of Galerkin approximations. Then we study stability properties of stationary solutions by using several approach methods. In the case of proportional delays, some sufficient conditions ensuring the polynomial stability in both mean square and almost sure senses will be provided.
Keywords: Stochastic globally modified Navier-Stokes equations, unbounded delays, stability, stationary solutions, polynomial stability
MSC numbers: Primary 60H15, 35Q35, 60H30, 35B35
Supported by: This work is financially supported by the Vietnam Ministry of Education and Training under grant number B2023-SPH-13.
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