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Time decay rate of weak solutions to the generalized MHD equations in R2

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  • Zhao, Caidi
  • Li, Bei

Abstract

This paper studies the time decay rate of weak solutions to the following two-dimensional magnetohydrodynamics (MHD) equations with fractional dissipations ∂tu+(u·∇)u−(b·∇)b+∇p=−(−▵)αu,∂tb+(u·∇)b−(b·∇)u=−(−▵)βb.The motivation is to understand how the parameters α and β affect the decay rate of its solutions. The authors use the Fourier splitting method of Schonbek to prove that the solutions have the following decay rate ∥u(x,t)∥2+∥b(x,t)∥2⩽c(1+t)1−2/γ,forlargeenought,where α, β ∈ [1, 2) and γ=max{α,β}.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:292:y:2017:i:c:p:1-8
    DOI: 10.1016/j.amc.2016.07.028
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    References listed on IDEAS

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    1. 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.
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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.

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