Stability of a strong viscous contact discontinuity in a free boundary problem for compressible Navier–Stokes equations. (October 2015)

• Record Type: Journal Article
• Authors: Zheng, Tingting
• Is Part Of: Nonlinear analysis. Volume 25(2015)
• Page Start: 238
• Page End: 257
• Publication Date: 2015-10
• Subjects: Free boundary problem -- Navier–Stokes equations -- Viscous contact discontinuity; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.03.001
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this study, we consider the nonlinear stability of a strong viscous contact discontinuity in a free boundary problem for the one-dimensional, full compressible Navier–Stokes equations in half space [ 0, ∞ ) . For the local stability of contact discontinuities, the local stability of a weak viscous contact discontinuity is well established, but for the global stability of an impermeable gas, fewer strong nonlinear wave stability results have been obtained, excluding zero dissipation or a γ → 1 gas. Thus, our main aim is to determine the corresponding nonlinear stability result using the elementary energy method. For a certain class of large perturbation, we show that the global stability result can be obtained for a strong viscous contact discontinuity in Navier–Stokes equations.