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Upper bound of decay rate for solutions to the Navier–Stokes–Voigt equations in R3

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  • Zhao, Caidi
  • Zhu, Hongjin

Abstract

In this paper, we first show the global existence, uniqueness and regularity of weak solutions for the Navier–Stokes–Voigt equations in R3. Then we combine the Fourier splitting method of Schonbek and the Gronwall inequality to prove that the solutions have the following decay rates‖∇mu(x,t)‖2+‖∇m+1u(x,t)‖2⩽c(1+t)-3/2-m,for largetwhen u0∈Hm(R3)∩L1(R3) and m=0,1.

Suggested Citation

  • Zhao, Caidi & Zhu, Hongjin, 2015. "Upper bound of decay rate for solutions to the Navier–Stokes–Voigt equations in R3," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 183-191.
    • Handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:183-191
    DOI: 10.1016/j.amc.2014.12.131
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    Cited by:

    1. Jingbo Wu & Qing-Qing Wang & Tian-Fang Zou, 2023. "Large Time Decay Rates of the 2D Micropolar Equations with Linear Velocity Damping," Mathematics, MDPI, vol. 11(10), pages 1-14, May.
    2. Zhao, Caidi & Li, Bei, 2017. "Time decay rate of weak solutions to the generalized MHD equations in R2," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 1-8.
    3. Yang, Xin-Guang & Li, Lu & Lu, Yongjin, 2018. "Regularity of uniform attractor for 3D non-autonomous Navier–Stokes–Voigt equation," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 11-29.

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