Abstract
In this chapter we consider the three-dimensional stationary Navier–Stokes equations with multivalued friction law boundary conditions on a part of the domain boundary. We formulate two existence theorems for the formulated problem. The first one uses the Kakutani–Fan–Glicksberg fixed point theorem, and the second one, with the relaxed assumptions, is based on the cut-off argument.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
C.C. Baniotopoulos, J. Haslinger, Z. Morávková, Mathematical modeling of delamination and nonmonotone friction problems by hemivariational inequalities. Appl. Math. 50, 1–25 (2005)
S. Carl, Existence and extremal solutions of parabolic variational-hemivariational inequalities. Monatsh. Math. 172, 29–54 (2013)
S. Carl, V.K. Le, D. Motreanu, Nonsmooth Variational Problems and Their Inequalities (Springer, New York, 2007)
N. Costea, V. Rǎdulescu, Inequality problems of quasi-hemivariational type involving set-valued operators and a nonlinear term. J. Glob. Optim. 52, 743–756 (2012)
J. Haslinger, M. Miettinen, P.D. Panagiotopoulos, Finite Element Method for Hemivariational Inequalities: Theory, Methods and Applications (Kluwer, Dordrecht, 1999)
S. Migórski, A. Ochal, Hemivariational inequalities for stationary Navier-Stokes equations. J. Math. Anal. Appl. 306, 197–217 (2005)
S. Migórski, A. Ochal, M. Sofonea, Nonlinear Inclusions and Hemivariational Inequalities. Models and Analysis of Contact Problems. Advances in Mechanics and Mathematics, vol. 26 (Springer, New York, 2013)
Z. Naniewicz, P.D. Panagiotopoulos, Mathematical Theory of Hemivariational Inequalities and Applications (Dekker, New York, 1995)
W. Pompe, Korn’s First Inequality with variable coefficients and its generalization. Comment. Math. Univ. Carol. 44, 57–70 (2003)
I. Šestak, B.S. Jovanović, Approximation of thermoelasticity contact problem with nonmonotone friction. Appl. Math. Mech. 31, 77–86 (2010)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Łukaszewicz, G., Kalita, P. (2016). Stationary Solutions of the Navier–Stokes Equations with Friction. In: Navier–Stokes Equations. Advances in Mechanics and Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-27760-8_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-27760-8_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-27758-5
Online ISBN: 978-3-319-27760-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)