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

Caidi Zhao and Bei Li

Applied Mathematics and Computation, 2017, vol. 292, issue C, 1-8

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}.

Keywords: Generalized MHD equations; Fractional dissipation; Time decay rate (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:292:y:2017:i:c:p:1-8

DOI: 10.1016/j.amc.2016.07.028

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