Decay Rates of global weak solutions for the MHD equations in\n \ mbox boldmathH^s(\ℝⁿ)

2017/03/19 by Robert Guterres, Guterres, Robert, Juliana R. Nunes +4
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1703.06453

openalex publication_date 2017/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that t^s/2 Vert ( \boldmath u, \boldmath\nb)(.,t) Vert_\H(\ℝⁿ) \→ 0, as t\→\n\∞ for Leray solutions ( \boldmath u, \boldmath b)(.,t)\nof the incompressible MHD equations, where 2 \≤ n \≤ 4 and s \≥ 0. As\na corollary of main result described previously we have also that\n\lim_t\→\∞ t^{\(n)/(2) - \(n)/(2q)} Vert( \boldmath\nu, \boldmath b)(.,t) Vert_L^q(\ℝⁿ) = 0, 2\≤ q\≤\n\∞.\n

Citations

• StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions

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