Global existence and asymptotic behavior for the 3D generalized Hall-MHD system. (March 2017)

• Record Type: Journal Article
• Authors: Wu, Xing; Yu, Yanghai; Tang, Yanbin
• Is Part Of: Nonlinear analysis. Volume 151(2017)
• Page Start: 41
• Page End: 50
• Publication Date: 2017-03
• Subjects: 35Q35 -- 35B65 -- 76W05; Generalized Hall-MHD equations -- Global existence -- Asymptotic behavior; 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.2016.11.010
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we consider the global existence for the 3D generalized Hall-MHD equations with fractional dissipative terms ( − Δ ) α u and ( − Δ ) α b under small initial data in the setting of Sobolev norms with lower regularity. For the global existence we enlarge the range of dissipative exponents α = β from ( 1, 7 6 ] to ( 1, 3 2 ), which established in a recent work. In addition, the long time behavior and rates of decay for both the solutions and higher derivatives in different Sobolev spaces are obtained by using the Fourier splitting method, which extends the previous work by Chae and Schonbek.