Large time behavior of solutions to the compressible Navier–Stokes equations around periodic steady states. (March 2017)

• Record Type: Journal Article
• Authors: Enomoto, Shota
• Is Part Of: Nonlinear analysis. Volume 152(2017)
• Page Start: 61
• Page End: 87
• Publication Date: 2017-03
• Subjects: Compressible Navier–Stokes equation -- Spatially periodic stationary solution -- Viscous Burgers equation -- Asymptotic behavior; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.12.007
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper shows that the strong solution to the compressible Navier–Stokes equation around spatially periodic stationary solution in a periodic layer of R n ( n = 2, 3 ) exists globally in time if Reynolds and Mach numbers are sufficiently small. It is proved that the asymptotic leading part of the perturbation is given by a solution to the one-dimensional viscous Burgers equation multiplied by a spatially periodic function when n = 2, and by a solution to the two-dimensional heat equation multiplied by a spatially periodic function when n = 3 .