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The 3D incompressible Navier–Stokes equations with partial hyperdissipation

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  • Wanrong Yang
  • Quansen Jiu
  • Jiahong Wu

Abstract

The three‐dimensional incompressible Navier–Stokes equations with the hyperdissipation (−Δ)γ always possess global smooth solutions when γ≥54. Tao [6] and Barbato, Morandin and Romito [1] made logarithmic reductions in the dissipation and still obtained the global regularity. This paper makes a different type of reduction in the dissipation and proves the global existence and uniqueness in the H1‐functional setting.

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  • Wanrong Yang & Quansen Jiu & Jiahong Wu, 2019. "The 3D incompressible Navier–Stokes equations with partial hyperdissipation," Mathematische Nachrichten, Wiley Blackwell, vol. 292(8), pages 1823-1836, August.
  • Handle: RePEc:bla:mathna:v:292:y:2019:i:8:p:1823-1836
    DOI: 10.1002/mana.201700176
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    Cited by:

    1. Ji, Ruihong & Luo, Wen & Jiang, Liya, 2023. "Stability of the 3D incompressible Navier–Stokes equations with fractional horizontal dissipation," Applied Mathematics and Computation, Elsevier, vol. 448(C).

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