Nonhomogeneous boundary value problem for Navier–Stokes equations in 2D symmetric unbounded domains. Issue 11 (18th August 2017)

• Record Type: Journal Article
• Authors: Kaulakytė, K.; Xue, W.
• Is Part Of: Applicable analysis. Volume 96:Issue 11(2017)
• Page Start: 1906
• Page End: 1927
• Publication Date: 2017-08-18
• Subjects: Stationary Navier–Stokes equations -- nonhomogeneous boundary value problem -- nonzero flux -- 2-dimensional domains with outlets to infinity -- symmetry; 35Q30 -- 35J65 -- 76D03 -- 76D05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1198780
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we study the nonhomogeneous boundary value problem for the stationary Navier–Stokes equations in two-dimensional symmetric domains with finitely many outlets to infinity. The domains may have no self-symmetric outlet ( -type domain), one self-symmetric outlet ( -type domain) or two self-symmetric outlets ( -type domain). We construct a symmetric solenoidal extension of the boundary value satisfying the Leray–Hopf inequality. After having such an extension, the nonhomogeneous boundary value problem is reduced to homogeneous one and the existence of at least one weak solution follows. Notice that we do not impose any restrictions on the size of the fluxes over the inner and outer boundaries. Moreover, the Dirichlet integral of the solution can be either finite or infinite depending on the geometry of the domains.