Abstract
AbstractWe study the Stokes eigenvalue problem under Navier boundary conditions in $$C^{1,1}$$
C
1
,
1
-domains $$\Omega \subset \mathbb {R}^3$$
Ω
⊂
R
3
. Differently from the Dirichlet boundary conditions, zero may be the least eigenvalue. We fully characterize the domains where this happens and we show that the ball is the unique domain where the zero eigenvalue is not simple, it has multiplicity three. We apply these results to show the validity/failure of a suitable Poincaré-type inequality. The proofs are obtained by combining analytic and geometric arguments.
Publisher
Springer Science and Business Media LLC
Reference21 articles.
1. Acevedo, P., Amrouche, C., Conca, C., Ghosh, A.: Stokes and Navier-Stokes equations with Navier boundary condition. C.R. Math. Acad. Sci. Paris 357, 115–119 (2019)
2. Amrouche, C., Rejaiba, A.: $$L^p$$-theory for Stokes and Navier-Stokes equations with Navier boundary condition. J. Diff. Eq. 256, 1515–1547 (2014)
3. Arioli, G., Gazzola, F., Koch, H.: Uniqueness and bifurcation branches for planar steady Navier-Stokes equations under Navier boundary conditions. J. Math. Fluid. Mech. 23, 49 (2021)
4. Beavers, G.S., Joseph, D.D.: Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207 (1967)
5. Beirão da Veiga, H., : Regularity for Stokes and generalized Stokes systems under nonhomogeneous slip-type boundary conditions. Adv. Diff. Eq. 9, 1079–1114 (2004)
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献