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Existence and long-time behavior of solutions to the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations with damping and memory
  • Nguyen Toan
Nguyen Toan
Haiphong University

Corresponding Author:ngduongtoanhp@gmail.com

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Abstract

In this paper, we study the long-time dynamical behavior of the non-autonomous velocity-vorticity-Voigt model of the 3D Navier-Stokes equations with damping and memory. We first investigate the existence and uniqueness of weak solutions to the initial boundary value problem for above-mentioned model. Next, we prove the existence of uniform attractor of this problem, where the time-dependent forcing term $f \in L^2_b(\mathbb{R}; H^{-1}(\Omega))$ is only translation bounded instead of translation compact. The results in this paper will extend and improve some results in Yue, Wang (Comput. Math. Appl., 2020) in the case of non-autonomous and contain memory kernels which have not been studied before.
06 Nov 2021Submitted to Mathematical Methods in the Applied Sciences
07 Nov 2021Submission Checks Completed
07 Nov 2021Assigned to Editor
12 Nov 2021Reviewer(s) Assigned
05 May 2022Review(s) Completed, Editorial Evaluation Pending
05 May 2022Editorial Decision: Revise Minor
09 May 20221st Revision Received
10 May 2022Submission Checks Completed
10 May 2022Assigned to Editor
10 May 2022Reviewer(s) Assigned
25 May 2022Review(s) Completed, Editorial Evaluation Pending
25 May 2022Editorial Decision: Accept