Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO STOCHASTIC 3D GLOBALLY MODIFIED NAVIER-STOKES EQUATIONS WITH UNBOUNDED DELAYS

  • Cung The Anh (Department of Mathematics Hanoi National University of Education) ;
  • Vu Manh Toi (Faculty of Computer Science and Engineering Thuyloi University) ;
  • Phan Thi Tuyet (Department of Mathematics Electric Power University)
  • Received : 2022.07.27
  • Accepted : 2023.12.28
  • Published : 2024.03.01
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Abstract

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-∞(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

Acknowledgement

This work is financially supported by the Vietnam Ministry of Education and Training under grant number B2023-SPH-13.

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