Weak solutions to the two-dimensional steady compressible Navier–Stokes equations. (April 2017)

• Record Type: Journal Article
• Authors: Zhong, Xin
• Is Part Of: Nonlinear analysis. Volume 34(2017)
• Page Start: 61
• Page End: 74
• Publication Date: 2017-04
• Subjects: Steady fluids -- Compressible Navier–Stokes system -- Viscous isothermal fluid -- Weak solution; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.08.004
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We study motions of the steady compressible viscous isothermal fluids in a bounded two dimensional domain governed by the Navier–Stokes equations. We obtain that there exists at least one weak solution to such a problem satisfying some integrability. The proof of this result is based on delicate estimates for the momentum equations and a bootstrapping argument.