Please use this identifier to cite or link to this item: http://dx.doi.org/10.25673/118514
Title: The Navier-Stokes equations on manifolds with boundary
Author(s): Shao, Yuanzhen
Simonett, GieriLook up in the Integrated Authority File of the German National Library
Wilke, MathiasLook up in the Integrated Authority File of the German National Library
Issue Date: 2025
Type: Article
Language: English
Abstract: We consider the motion of an incompressible viscous fluid on a compact Riemannian manifold Mwith boundary. The motion on Mis modeled by the incompressible Navier-Stokes equations, and the fluid is sub-ject to pure or partial slip boundary conditions of Navier type on ∂M. We establish existence and uniqueness of strong as well as weak (variational) solutions for initial data in critical spaces. Moreover, we show that the set of equilibria consists of Killing vector fields on Mthat satisfy corresponding boundary conditions, and we prove that all equilibria are (locally) stable. In case Mis two-dimensional we show that solutions with divergence free initial condition in L2(M; TM)exist globally and converge to an equilibrium exponen-tially fast.
URI: https://opendata.uni-halle.de//handle/1981185920/120472
http://dx.doi.org/10.25673/118514
Open Access: Open access publication
License: (CC BY 4.0) Creative Commons Attribution 4.0(CC BY 4.0) Creative Commons Attribution 4.0
Journal Title: Journal of differential equations
Publisher: Elsevier
Publisher Place: Orlando, Fla.
Volume: 416
Issue: 2
Original Publication: 10.1016/j.jde.2024.10.030
Page Start: 1602
Page End: 1659
Appears in Collections:Open Access Publikationen der MLU

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