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Article information
2002 , Volume 7, ¹ 1, p.83-95
Krachmar S.
Channel flows and steady variational inequalities of the Navier-Stokes type
We study a steady flow of a viscous incompressible fluid in a channel with a non-Dirichlet boundary condition on the output. In order to control the kinetic energy of the fluid in the channel, we assume that possible backward flows on the output are in some sense bounded. Flow fields which satisfy this assumption fill up a convex subset of a certain function space. We formulate a variational inequality of the Navier-Stokes type on this convex set and we prove the existence of its weak solution. Moreover, we also study the question in which sense the weak solution satisfies the Navier-Stokes equations and the mixed boundary condition if the solution is smooth.
[full text] Classificator Msc2000:- *35Q30 Stokes and Navier-Stokes equations
- 76D03 Existence, uniqueness, and regularity theory
- 76M30 Variational methods
Keywords: continuous trace operator, Stokes theorem, Galerkin method, method of penalisation, Holder inequality
Author(s):
Krachmar St
Office: Czech Technical University, Prague
Address: Czech, Prague
E-mail: kracmar@marian.fsik.cvut.cz
Bibliography link:
Krachmar S. Channel flows and steady variational inequalities of the Navier-Stokes type // Computational technologies. 2002. V. 7. ¹ 1. P. 83-95
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