Stationary solutions to outflow problem for 1-D compressible fluid models of Korteweg type: Existence, stability and convergence rate. (June 2020)

• Record Type: Journal Article
• Authors: Hong, Hakho
• Is Part Of: Nonlinear analysis. Volume 53(2020)
• Publication Date: 2020-06
• Subjects: Navier–Stokes–Korteweg system -- outflow problem -- stationary solution -- convergence rate -- Stability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.103055
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we are concerned with the outflow problem in the half line ( 0, ∞ ) to the isothermal compressible Navier–Stokes–Korteweg system with a nonlinear boundary condition for vanishing capillary tensor at x = 0 . We first give some necessary and sufficient conditions for the existence of the stationary solutions with the aid of center manifold theory. We also show the stability of the stationary solutions under smallness assumptions on the initial perturbation in the Sobolev space, by employing an energy method. Moreover, the convergence rate of the solution toward the stationary solutions is obtained, provided that the initial perturbations belong to the weighted Sobolev spaces.