E ) est relativement compact pour la topologie forte. En d'autres termes, on dit que T est compact si, pour toute suite bornée (x n ), p.la suite (T ,
, Théorème 5.22 (Théorème de point fixe de Schauder)
Soit T une application continue de Z dans Z telle que T (Z) est relativement compacte ,
Sobolev spaces, 1975. ,
Théorie des semi-groupes pour les équations de Stokes et de Navier-Stokes avec des conditions aux limites de type Navier, thèse de doctorat à l, 2015. ,
Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension, Czechoslovak Mathematical Journal, vol.44, pp.109-140, 1994. ,
On the Stokes equations with the Navier-type boundary conditions, Differential Equations & Applications, vol.3, issue.4, pp.581-607, 2011. ,
DOI : 10.7153/dea-03-36
Mixed formulation for Stokes problem with Tresca friction, Comptes Rendus Mathematique de l'Académie des sciences, pp.1069-1072, 2010. ,
Variational and quasivariational inequalities applications to free boundary problems, 1984. ,
A review of the slip (wall depletion) of polymer solutions, emulsions and particle suspensions in viscometers: its cause, character, and cure, Journal of Non-Newtonian Fluid Mechanics, vol.56, issue.3, pp.221-251, 1995. ,
DOI : 10.1016/0377-0257(94)01282-M
On a free boundary problem for the Reynolds equation derived from the Stokes system with Tresca boundary conditions, Journal of Mathematical Analysis and Applications, vol.282, issue.1, pp.212-231, 2003. ,
DOI : 10.1016/S0022-247X(03)00140-9
URL : https://hal.archives-ouvertes.fr/hal-00454697
Existence result for a strongly coupled problem with heat convection term and Tresca's law, Journal of Advanced Research in Differential Equations, vol.3, pp.33-53, 2011. ,
Espaces topologiques : Fonctions multivoques, 1966. ,
Non-linear elliptic and parabolic equations involving measure data, Journal of Functional Analysis, vol.87, issue.1, pp.149-169, 1989. ,
DOI : 10.1016/0022-1236(89)90005-0
Asymptotic analysis of solutions of a thin film lubrication problem with Coulomb fluid???solid interface law, International Journal of Engineering Science, vol.41, issue.6, pp.521-537, 2003. ,
DOI : 10.1016/S0020-7225(02)00282-3
ON A LUBRICATION PROBLEM WITH FOURIER AND TRESCA BOUNDARY CONDITIONS, Mathematical Models and Methods in Applied Sciences, vol.76, issue.06, pp.913-941, 2004. ,
DOI : 10.1115/1.2920631
On a non-isothermal, non-Newtonian lubrication problem with Tresca law: Existence and the behavior of weak solutions, Nonlinear Analysis: Real World Applications, vol.9, issue.2, pp.674-692, 2008. ,
DOI : 10.1016/j.nonrwa.2006.12.012
Non-isothermal Navier-Stokes system with mixed boundary conditions and friction law : uniqueness and regularity properties, Nonlinear Analysis : Theory, Methods and Applications, vol.102, pp.168-185, 2014. ,
Existence for non-isothermal fluid flows with Tresca's friction and Cattaneo's heat law, Journal of Mathematical Analysis and Applications, vol.427, issue.1, pp.499-514, 2015. ,
DOI : 10.1016/j.jmaa.2015.02.034
Unsteady 3D-Navier-Stokes system with Tresca's friction law, 2015. ,
Etude théorique et numérique de quelques problèmes d'écoulements et de chaleur hyperbolique, thèse de doctorat à l, 2012. ,
Analyse de quelques problèmes aux limites en mécanique des milieux continus, thèse de doctorat à l, 2013. ,
Mathematical tools for the study of the incompressible Navier-Stokes equations and related models, Applied Mathematical Sciences, vol.183, 2013. ,
DOI : 10.1007/978-1-4614-5975-0
URL : https://hal.archives-ouvertes.fr/hal-00777731
Analyse fonctionnelle théorie et applications, 1999. ,
Introduction aux problèmes d'évolution semilinéaires , Ellipses, Société de Mathématiques Appliquées et Industrielles, 1990. ,
Mathematical elasticity, Volume I : Three-dimensional elasticity, Studies in Mathematics and its Applications, 1988. ,
Existence for a Class of Non???Newtonian Fluids with a Nonlocal Friction Boundary Condition, Acta Mathematica Sinica, English Series, vol.2, issue.2, pp.523-534, 2006. ,
DOI : 10.1017/S0027763000004323
Introduction to the calculus of variations, 2004. ,
Espaces fonctionnels, Utilisation dans la résolution des équations aux dérivées partielles, EDP Sciences, 2007. ,
Functional spaces for the theory of elliptic partial differential equations ,
DOI : 10.1007/978-1-4471-2807-6
Hitchhiker's guide to the fractional Sobolev spaces, Bulletin des Sciences Mathématiques, vol.136, pp.521-573, 2012. ,
Intégration et espaces de Sobolev à valeurs vectorielles, 2001. ,
Quelques résultats sur les espaces de Sobolev, 2001. ,
Les inéquations en mécanique et physique, 1972. ,
Slip and friction of polymer melt flows, Rheology Series, vol.5, pp.357-388, 1996. ,
DOI : 10.1016/S0169-3107(96)80013-X
Non-isothermal, non-Newtonian Hele???Shaw flows within Cattaneo???s heat flux law, Mathematical and Computer Modelling, vol.46, issue.5-6, pp.765-775, 2007. ,
DOI : 10.1016/j.mcm.2006.12.005
, J. Faraut. Calcul intégral, EDP Sciences, 2006.
Implementation of a slip boundary condition in a finite volume code aimed to predict fluid flows, II Conferência Nacional de Métodos Numéricos em Mecânica de Fluidos e Termodinâmica, pp.8-9, 2008. ,
Navier-Stokes equations and turbulence, 2001. ,
DOI : 10.1017/CBO9780511546754
Théorie analytique de la chaleur, Firmin Didot, père et fils, p.1822 ,
Cours de lubrification, pp.0-1 ,
A mathematical analysis of motions of viscous incompressible fluid under leak or slip boundary conditions, Mathematical Fluid Mechanics and Modeling, vol.888, pp.199-216, 1994. ,
Analytical and numerical approaches to stationary flow problems with leak and slip boundary conditions, Advances in Numerical Mathematics, vol.14, pp.17-31, 1994. ,
Variational inequalities for the Stokes equation with boundary conditions of friction type, Recent Developments in Domain Decomposition Methods and Flow Problems, pp.15-33, 1998. ,
Non-stationary Stokes flows under leak boundary conditions of friction type, Journal of Computational and Applied Mathematics, vol.19, pp.1-8, 2001. ,
Remarks on the Stokes flows under slip and leak boundary conditions of friction type, Topics in Mathematical Fluid Mechanics, vol.10, pp.73-94, 2002. ,
A coherent analysis of Stokes flows under boundary conditions of friction type, Journal of Computational and Applied Mathematics, vol.149, issue.1, pp.57-69, 2002. ,
DOI : 10.1016/S0377-0427(02)00520-4
Elliptic partial differential equations of second order, A Series of, Comprehensive Studies in Mathematics, 1977. ,
Finite element approximation of the Navier Stokes equations, 1986. ,
DOI : 10.1007/BFb0063447
Flow with slip at the wall : from simple to complex fluids, Comptes Rendus Physique de l'Académie des Sciences, pp.241-249, 2003. ,
The initial value problem for the non-homogeneous Navier???Stokes equations with general slip boundary condition, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.130, issue.04, pp.827-835, 2000. ,
DOI : 10.1017/S0308210500000457
Contact problems in elasticity : a study of variational inequalities and finite element methods, 1988. ,
DOI : 10.1137/1.9781611970845
Approximations variationelles de problèmes aux limites elliptiques et éléments finis, 2003. ,
Equations aux dérivées partielles non linéaires, Mathématiques et Applications, vol.72, 2013. ,
Mathématiques des modèles multi-échelles, 2013. ,
Steady flows of incompressible Newtonian fluids with threshold slip boundary conditions, Mathematical Analysis in Fluid and Gas Dynamics, vol.1353, pp.21-34, 2004. ,
STEADY STOKES FLOWS WITH THRESHOLD SLIP BOUNDARY CONDITIONS, Mathematical Models and Methods in Applied Sciences, vol.88, issue.08, pp.1141-1168, 2005. ,
DOI : 10.1017/CBO9780511897450
Steady solutions of the Navier?Stokes equations with threshold slip boundary conditions, Mathematical Methods in the Applied Sciences, vol.30, pp.595-624, 2007. ,
Quelques méthodes de résolution des problèmes aux limites non linéaires, 1969. ,
On Some Problems Connected with Navier Stokes Equations, pp.59-84, 1978. ,
DOI : 10.1016/B978-0-12-195250-1.50008-4
Note du cours éléments finis, 2011. ,
Compressible fluid flow and systems of conservation laws in several space variables, Applied Mathematical Sciences, vol.53, 1984. ,
DOI : 10.1007/978-1-4612-1116-7
Steady-state thermal Herschel- Bulkley flow with Tresca's friction law, Electronic Journal of Differential Equations, vol.2010, pp.1-14, 2010. ,
Équations elliptiques non linéaires avec second membre L 1 ou mesure, 26 éme Congrés National d'Analyse numérique, 1994. ,
Mémoire sur les lois du mouvement des fluides, Mémoires de l'Académie Royale des Sciences de l, pp.389-440, 1822. ,
Boundary slip in Newtonian liquids: a review of experimental studies, Reports on Progress in Physics, vol.68, issue.12, pp.2859-2897, 2005. ,
DOI : 10.1088/0034-4885/68/12/R05
The Navier-Stokes equation with slip boundary conditions, Mathematical Analysis in Fluid and Gas Dynamics, vol.1536, pp.46-57, 2007. ,
,
Qualitative methods in non linear mechanics, 1986. ,
Effect of solid properties on slip at a fluid-solid interface, Physical Review E, vol.83, issue.2, p.21602, 2011. ,
DOI : 10.1126/science.1147550
Friction and slip of a simple liquid at solide surface, Tribology Letters, vol.7, issue.2/3, pp.147-152, 1999. ,
DOI : 10.1023/A:1019161101812
The effect of the slip boundary condition on the flow of fluids in a channel, Acta Mechanica, vol.734, issue.3-4, pp.113-126, 1999. ,
DOI : 10.1007/3-540-11948-5_66
Equations de Stokes et de Navier-Stokes avec des conditions aux limites de Navier, thèse de doctorat à l, 2014. ,
Sur quelques problèmes de lubrification par des fluides newtoniens non isothermes avec des conditions aux bords non linéaires. Etude mathématique et numérique, thèse de doctorat à l, 2005. ,
Non-Newtonian flow in a thin film with boundary conditions of Coulomb's type, ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, pp.702-721, 2006. ,
DOI : 10.1080/10236190108808258
Compact sets in the space L p (0, Annali di Matematica Pura ed Applicata, pp.65-95, 1987. ,
Slip at Fluid-Solid Interface, Polymer Reviews, vol.38, issue.4, pp.309-340, 2011. ,
DOI : 10.1122/1.550528
On a strong solution of the non-stationary Navier?Stokes equations under slip or leak boundary conditions of friction type, Journal of Differential Equations, vol.254, pp.756-778, 2013. ,
The initial value problem for the equations of motion of general fluids with general slip boundary condition, Mathematical Analysis of Fluid and Plasma Dynamics, vol.734, pp.123-142, 1990. ,
The initial value problem for the Navier- Stokes equations with general slip boundary condition, Journal of Advanced Mathematics and Applications, vol.4, pp.51-69, 1994. ,
Navier Stokes Equations: Theory and Numerical Analysis, Journal of Applied Mechanics, vol.45, issue.2, 1979. ,
DOI : 10.1115/1.3424338
Apparent fluid slip at hydrophobic microchannel walls, Physics of Fluids, vol.381, issue.3, pp.9-12, 2002. ,
DOI : 10.1115/1.483256
Mécanique des fluides appliquée : écoulements incompressibles dans les circuits, canaux et rivières, autour des structures et dans l'environnement, 1998. ,
On Korn's inequality, Journal of Computational Mathematics, vol.21, pp.321-324, 2003. ,
Fluid mechanics, 2002. ,