Stability of composite wave for inflow problem on the planar magnetohydrodynamics. (December 2018)

• Record Type: Journal Article
• Authors: Yin, Haiyan
• Is Part Of: Nonlinear analysis. Volume 44(2018)
• Page Start: 305
• Page End: 333
• Publication Date: 2018-12
• Subjects: Magnetohydrodynamics -- Composite wave -- Inflow problem -- Stability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.05.008
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we investigate the large time behavior of the solutions to an initial–boundary value problem for the planar magnetohydrodynamics in a half line R + ≔ ( 0, ∞ ) . Inspired by the relationship between magnetohydrodynamics and Navier–Stokes, we can prove that the composite wave consisting of the subsonic BL-solution, the contact wave, and the rarefaction wave for the inflow problem on the planar magnetohydrodynamics is time-asymptotically stable. Meanwhile, we obtain the global existence of solutions based on the basic energy method by taking into account the complexity of composite wave.