Asymptotic decay of solutions to 3D MHD equations. (February 2016)

• Record Type: Journal Article
• Authors: Wang, Yinxia
• Is Part Of: Nonlinear analysis. Volume 132(2016)
• Page Start: 115
• Page End: 125
• Publication Date: 2016-02
• Subjects: 35Q35 -- 35K15; MHD equations -- Initial value problem -- Asymptotic behavior -- Stability; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.11.002
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In the very recent work Wang and Wang (2014) proved that the initial value problem for the three dimension incompressible MHD equations has a global solutions ( u, B ) ∈ C ( [ 0, ∞ ) ; χ − 1 ), provided that the norms of the initial data are bounded exactly by the minimal value of the viscosity coefficients. In this paper, we prove that global solutions u, B that was obtained in Wang and Wang (2014) is asymptotic to zero in sense of the norm of the space χ − 1 as time goes to infinity. Moreover, stability of global solutions is also discussed.