论文信息 - A PROOF OF THE INF–SUP CONDITION FOR THE STOKES EQUATIONS ON LIPSCHITZ DOMAINS

A PROOF OF THE INF–SUP CONDITION FOR THE STOKES EQUATIONS ON LIPSCHITZ DOMAINS

The purpose of this paper is to present a rather simple proof of an inequality of Necas9 which is equivalent to the inf–sup condition. This inequality is fundamental in the study of the Stokes equations. The boundary of the domain is only assumed to be Lipschitz.

James H. Bramble

[1] J. Nitsche. On Korn's second inequality , 1981 .

[2] Équations de Navier-Stokes , 1960 .

[3] 川口光年,et al. O. A. Ladyzhenskaya: The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach Sci. Pub. New York-London, 1963, 184頁, 15×23cm, 3,400円. , 1964 .

[4] G. Fichera. Sull'esistenza e sul calcolo delle soluzioni dei problemi al contorno, relativi all'equilibrio di un corpo elastico , 1950 .

[5] Vivette Girault,et al. Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms , 1986, Springer Series in Computational Mathematics.

[6] R. Temam. Navier-Stokes Equations , 1977 .

[7] Michel Fortin,et al. Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[8] J. Lions,et al. Inequalities in mechanics and physics , 1976 .