Y. Achdou and O. Pironneau, Domain decomposition and wall laws, C. R. Acad. Sci. Paris Sér. I Math, vol.320, issue.5, pp.541-547, 1995.

Y. Achdou, O. Pironneau, and F. Valentin, Effective Boundary Conditions for Laminar Flows over Periodic Rough Boundaries, Journal of Computational Physics, vol.147, issue.1, pp.187-218, 1998.
DOI : 10.1006/jcph.1998.6088

Y. Achdou, O. Pironneau, and F. Valentin, Shape control versus boundary control, Équations aux dérivées partielles et applications, pp.1-18, 1998.

F. Alliot and C. Amrouche, : AN APPROACH IN WEIGHTED SOBOLEV SPACES, Mathematical Models and Methods in Applied Sciences, vol.19, issue.05, pp.723-754, 1999.
DOI : 10.1007/BF00995142

F. Alliot and C. Amrouche, Weak solutions for the exterior Stokes problem in weighted Sobolev spaces, Mathematical Methods in the Applied Sciences, vol.37, issue.6, pp.575-600, 2000.
DOI : 10.1007/BF00995142

C. Amrouche and V. Girault, Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension, Czechoslovak Math. J, vol.44, issue.1191, pp.109-140, 1994.

C. Amrouche, V. Girault, and J. Giroire, Weighted Sobolev spaces for Laplace's equation in R n, J. Math. Pures Appl, issue.96, pp.73579-606, 1994.

C. Amrouche, V. Girault, and J. Giroire, Dirichlet and neumann exterior problems for the n-dimensional laplace operator an approach in weighted sobolev spaces, Journal de Math??matiques Pures et Appliqu??es, vol.76, issue.1, pp.55-81, 1997.
DOI : 10.1016/S0021-7824(97)89945-X

URL : https://doi.org/10.1016/s0021-7824(97)89945-x

C. Amrouche and M. Meslameni, Stokes problem with several types of boundary conditions in an exterior domain, Electron. J. Differential Equations, issue.196, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00985042

C. Amrouche and A. Rejaiba, -theory for Stokes and Navier???Stokes equations with Navier boundary condition, Journal of Differential Equations, vol.256, issue.4, pp.1515-1547, 2014.
DOI : 10.1016/j.jde.2013.11.005

C. Amrouche and A. Rejaiba, Navier-Stokes equations with Navier boundary condition, Mathematical Methods in the Applied Sciences, vol.23, issue.119, pp.5091-5112, 2016.
DOI : 10.1142/S0218202512500455

URL : https://hal.archives-ouvertes.fr/hal-01581286

A. Basson and D. Gérard-varet, Wall laws for fluid flows at a boundary with random roughness, Communications on Pure and Applied Mathematics, vol.98, issue.7, pp.941-987, 2008.
DOI : 10.1007/978-3-642-84659-5

URL : https://hal.archives-ouvertes.fr/hal-00083222

H. Beirão-da and . Veiga, Regularity for Stokes and generalized Stokes systems under nonhomogeneous sliptype boundary conditions, Adv. Differential Equations, vol.9, pp.9-101079, 2004.

H. Beirão and . Veiga, Vorticity and regularity for flows under the Navier boundary condition, Commun. Pure Appl. Anal, vol.5, issue.4, pp.907-918, 2006.

S. K. Bhowmik, R. Belbaki, T. Z. Boulmezaoud, and S. Mziou, Solving two dimensional second order elliptic equations in exterior domains using the inverted finite elements method, Computers & Mathematics with Applications, vol.72, issue.9, pp.2315-2333, 2016.
DOI : 10.1016/j.camwa.2016.08.030

T. Z. Boulmezaoud, Inverted finite elements: a new method for solving elliptic problems in unbounded domains, ESAIM: Mathematical Modelling and Numerical Analysis, vol.5, issue.1, pp.109-145, 2005.
DOI : 10.1016/0165-2125(83)90016-1

URL : http://www.esaim-m2an.org/articles/m2an/pdf/2005/01/m2an0379.pdf

T. Z. Boulmezaoud, K. Kaliche, and N. Kerdid, Inverted finite elements for div-curl systems in the whole space, Advances in Computational Mathematics, vol.27, issue.4, pp.1469-1489, 2017.
DOI : 10.1016/S0168-9274(98)00025-7

T. Z. Boulmezaoud, S. Mziou, and T. Boudjedaa, Numerical Approximation of Second-Order Elliptic Problems in Unbounded Domains, Journal of Scientific Computing, vol.140, issue.3???4, pp.295-312, 2014.
DOI : 10.1016/S0045-7825(96)01010-9

J. Casado-díaz, E. Fernández-cara, and J. Simon, Why viscous fluids adhere to rugose walls:, Journal of Differential Equations, vol.189, issue.2, pp.526-537, 2003.
DOI : 10.1016/S0022-0396(02)00115-8

P. G. Ciarlet and P. Ciarlet-jr, ANOTHER APPROACH TO LINEARIZED ELASTICITY AND A NEW PROOF OF KORN'S INEQUALITY, Mathematical Models and Methods in Applied Sciences, vol.28, issue.02, pp.259-271, 2005.
DOI : 10.1023/A:1022945123237

E. Friedmann, The Optimal Shape of Riblets in the Viscous Sublayer, Journal of Mathematical Fluid Mechanics, vol.12, issue.2, pp.243-265, 2010.
DOI : 10.1007/s00021-008-0284-z

E. Friedmann and T. Richter, Optimal Microstructures Drag Reducing Mechanism of Riblets, Journal of Mathematical Fluid Mechanics, vol.228, issue.4, pp.429-447, 2011.
DOI : 10.1007/978-3-642-85829-1

URL : http://cemat.ist.utl.pt/gpgaldi/abs/friedmann.pdf

G. P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations Tracts in Natural Philosophy, 1994.

G. P. Galdi and C. G. Simader, Existence, uniqueness and Lq-estimates for the stokes problem in an exterior domain, Archive for Rational Mechanics and Analysis, vol.53, issue.3, pp.291-318, 1990.
DOI : 10.1007/BF01084616

G. P. Galdi and C. G. Simader, New estimates for the steady-state Stokes problem in exterior domains with applications to the Navier-Stokes problem, Differential Integral Equations, vol.7, pp.3-4847, 1994.

D. Gérard-varet and N. Masmoudi, Relevance of the Slip Condition for Fluid Flows Near an Irregular Boundary, Communications in Mathematical Physics, vol.19, issue.2, pp.99-137, 2010.
DOI : 10.1007/s00220-002-0738-8

V. Girault, The gradient, divergence, curl and Stokes operators in weighted Sobolev spaces of R 3, J. Fac. Sci. Univ. Tokyo Sect. IA Math, vol.39, issue.2, pp.279-307, 1992.

V. Girault, The Stokes problem and vector potential operator in three-dimensional exterior domains: an approach in weighted Sobolev spaces, Differential Integral Equations, vol.7, issue.2, pp.535-570, 1994.

V. Girault, J. Giroire, and A. Sequeira, A stream-function-vorticity variational formulation for the exterior Stokes problem in weighted Sobolev spaces, Mathematical Methods in the Applied Sciences, vol.8, issue.5, pp.345-363, 1992.
DOI : 10.1007/978-3-642-61623-5

V. Girault and P. A. Raviart, Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms, 1986.

V. Girault and A. Sequeira, A well-posed problem for the exterior Stokes equations in two and three dimensions, Archive for Rational Mechanics and Analysis, vol.8, issue.133, pp.313-333, 1991.
DOI : 10.1007/978-3-642-61623-5

J. Giroire, Étude de quelques problèmes aux limites extérieurs et résolution par équations intégrales, Thèse de Doctorat d'État, 1987.

B. Hanouzet, Espaces de Sobolev avec poids Application au problème de Dirichlet dans un demi espace, Rend. Sem. Mat. Univ. Padova, vol.46, pp.227-272, 1971.

W. Jäger and A. Mikeli´cmikeli´c, On the Roughness-Induced Effective Boundary Conditions for an Incompressible Viscous Flow, Journal of Differential Equations, vol.170, issue.1, pp.96-122, 2001.
DOI : 10.1006/jdeq.2000.3814

D. Daniel, G. S. Joseph, and . Beavers, Boundary conditions at a naturally permeable wall, J. Fluid Mech, vol.30, pp.197-207, 1967.

V. A. Kondratiev and O. A. Ole?-inik, Boundary value problems for a system in elasticity theory in unbounded domains, Korn inequalities. Uspekhi Mat. Nauk, pp.55-98, 1988.

H. Kozono and H. Sohr, On a new class of generalized solutions for the Stokes equations in exterior domains, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.19, issue.42, pp.155-181, 1992.

A. Kufner, Weighted Sobolev spaces, 1985.

J. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Travaux et Recherches Mathématiques, 1968.

H. Louati, M. Meslameni, and U. Razafison, Weighted L p -theory for vector potential operators in threedimensional exterior domains, Math. Methods Appl. Sci, vol.39, issue.8, 1990.
DOI : 10.1002/mma.3615

URL : https://hal.archives-ouvertes.fr/hal-01025281

G. Mulone and F. Salemi, On the existence of hydrodynamic motion in a domain with free boundary type conditions, Meccanica, vol.34, issue.3, pp.136-144, 1983.
DOI : 10.1007/BF02128580

G. Mulone and F. Salemi, On the hydrodynamic motion in a domain with mixed boundary conditions: Existence, uniqueness, stability and linearization principle, Annali di Matematica Pura ed Applicata, vol.47, issue.n. 6, pp.147-174, 1985.
DOI : 10.1007/978-3-642-65711-5

C. L. Navier, Mémoire sur les Lois du Mouvement des fluides, Mem. Acad. Sci. Inst. de France, pp.389-440, 1827.

A. Russo and A. Tartaglione, On the Navier problem for the stationary Navier???Stokes equations, Journal of Differential Equations, vol.251, issue.9, pp.2387-2408, 2011.
DOI : 10.1016/j.jde.2011.07.001

J. Serrin, Mathematical Principles of Classical Fluid Mechanics, Handbuch der Physik (herausgegeben von S. Flügge), Bd. 8/1, Strömungsmechanik I (Mitherausgeber C. Truesdell), pp.125-263, 1959.
DOI : 10.1007/978-3-642-45914-6_2

V. A. Solonnikov and V. E. Scadilov, A certain boundary value problem for the stationary system of Navier- Stokes equations, Trudy Mat. Int. Steklov, vol.125, pp.1515-1547235, 1973.

M. Specovius-neugebauer, Exterior stokes problems and decay at infinity, Mathematical Methods in the Applied Sciences, vol.125, issue.1, pp.351-367, 1986.
DOI : 10.1080/0360530810882192

M. Specovius-neugebauer, Weak solutions of the Stokes problem in weighted Sobolev spaces, Acta Applicandae Mathematicae, vol.15, issue.1-2, pp.195-203, 1994.
DOI : 10.1007/BF00995141