Convergence rate of solutions toward stationary solutions to a two-phase model with magnetic field in a half line. (February 2020)

• Record Type: Journal Article
• Authors: Yin, Haiyan; Zhu, Limei
• Is Part Of: Nonlinear analysis. Volume 51(2020)
• Publication Date: 2020-02
• Subjects: Two-phase model with magnetic field -- Stationary solutions -- Convergence rates -- Weighted energy method; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.05.004
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we study an asymptotic behavior of a solution to the outflow problem for a two-phase model with magnetic field. Our idea mainly comes from[1] and [2] which investigate the asymptotic stability and convergence rates of stationary solutions to the outflow problem for an isentropic Navier–Stokes equation. For the two-phase model with magnetic field, we also obtain the asymptotic stability and convergence rates of global solutions towards corresponding stationary solutions if the initial perturbation belongs to the weighted Sobolev space. The proof is based on the weighted energy method.