Existence of suitable weak solutions to the Navier–Stokes equations in time varying domains. (November 2017)

• Record Type: Journal Article
• Authors: Choe, Hi Jun; Jang, Yunsoo; Yang, Minsuk
• Is Part Of: Nonlinear analysis. Volume 163(2017)
• Page Start: 163
• Page End: 176
• Publication Date: 2017-11
• Subjects: 35k20 -- 35A01 -- 35D30; Navier–Stokes equations -- Suitable weak solution -- Localized energy estimate; 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.2017.08.003
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider suitable weak solutions to the Navier–Stokes equations in time varying domains. We develop Schauder theory for the approximate Stokes equations in time varying domains whose solutions satisfy a uniform localized energy estimate including boundary. Existence of suitable weak solutions in time varying domains follows from compactness in Lebesgue and Sobolev spaces.