Global existence, uniqueness and exponential stability of solutions for the one-dimensional Navier–Stokes equations with capillarity. (April 2021)

• Record Type: Journal Article
• Authors: Qin, Yuming; Zhang, Jianlin; Wang, Yang; Su, Xing
• Is Part Of: Nonlinear analysis. Volume 58(2021)
• Publication Date: 2021-04
• Subjects: Navier–Stokes equations -- Capillarity -- Korteweg stress tensor; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103222
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we investigate non-isothermal one-dimensional model of capillary compressible fluids as derived by Slemrod (1984) and Dunn and Serrin (1985). We establish the global existence, uniqueness and exponential stability of strong solutions in H + i ( i = 1, 2, 4 ) for the one-dimensional Navier–Stokes equations with capillarity, which implies the existence and exponential stability of the nonlinear C 0 -semigroups S ( t ) on H + i ( i = 1, 2, 4 ) .