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October 2022 Asymptotic behavior of solutions on modifications of three-dimensional Navier–Stokes equations with unbounded delays
Le Thi Thuy
Rocky Mountain J. Math. 52(5): 1775-1794 (October 2022). DOI: 10.1216/rmj.2022.52.1775

Abstract

We consider modifications of 3D Navier–Stokes equations involving unbounded delays in Ω3. First, we show the existence and uniqueness of weak solutions by the Galerkin approximations method and energy method. Second, we prove the existence and uniqueness of stationary solutions by the Brouwer fixed point theorem. Finally, we study the stability of stationary solutions by the classical directly approach and construction of Lyapunov function. We also give a sufficient condition for the polynomial stability and polynomial decay of the stationary solutions in some special cases of unbounded variable delays.

Citation

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Le Thi Thuy. "Asymptotic behavior of solutions on modifications of three-dimensional Navier–Stokes equations with unbounded delays." Rocky Mountain J. Math. 52 (5) 1775 - 1794, October 2022. https://doi.org/10.1216/rmj.2022.52.1775

Information

Received: 18 May 2021; Revised: 4 November 2021; Accepted: 10 January 2022; Published: October 2022
First available in Project Euclid: 28 November 2022

Digital Object Identifier: 10.1216/rmj.2022.52.1775

Subjects:
Primary: 35D30 , 35Q30

Keywords: asymptotic a priori estimate method , asymptotically stable , delays , local stability , modified Navier–Stokes equation , polynomial decay , polynomial stable , stationary solution , Weak solution

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 5 • October 2022
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