P. Acevedo, C. Amrouche, C. Conca, and A. Ghosh, Stokes and Navier?Stokes equations with Navier boundary condition, Comptes Rendus Mathematique, vol.357, issue.2, pp.115-119, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02494785

F. Alliot and C. Amrouche, THE STOKES PROBLEM IN ?n: AN APPROACH IN WEIGHTED SOBOLEV SPACES, Mathematical Models and Methods in Applied Sciences, vol.09, issue.05, pp.723-754, 1999.

F. Alliot and C. Amrouche, Weak solutions for the exterior Stokes problem in weighted Sobolev spaces, Mathematical Methods in the Applied Sciences, vol.23, issue.6, pp.575-600, 2000.

C. Amrouche and V. Girault, Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension, Czechoslovak Mathematical Journal, vol.44, issue.1, pp.109-140, 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 Mathématiques Pures et Appliquées, vol.76, issue.1, pp.55-81, 1997.

C. Amrouche, M. Meslameni, and ?. Ne?asová, The stationary Oseen equations in an exterior domain: An approach in weighted Sobolev spaces, Journal of Differential Equations, vol.256, issue.6, pp.1955-1986, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00985038

C. Amrouche and A. Rejaiba, Stationary Stokes equations with friction slip boundary conditions, Twelfth International Conference Zaragoza-Pau on Mathematics, vol.39, pp.23-32, 2014.

C. Amrouche and A. Rejaiba, Lp-theory for Stokes and Navier?Stokes equations with Navier boundary condition, Journal of Differential Equations, vol.256, issue.4, pp.1515-1547, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00985041

C. Amrouche and A. Rejaiba, Navier-Stokes equations with Navier boundary condition, Mathematical Methods in the Applied Sciences, vol.39, issue.17, pp.5091-5112, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01581286

C. Amrouche and M. Á. Rodríguez-bellido, Stationary Stokes, Oseen and Navier?Stokes Equations with Singular Data, Archive for Rational Mechanics and Analysis, vol.199, issue.2, pp.597-651, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00549166

C. Amrouche, ?. Ne?asová, and Y. Raudin, From Strong to Very Weak Solutions to the Stokes System with Navier Boundary Conditions in the Half-Space, SIAM Journal on Mathematical Analysis, vol.41, issue.5, pp.1792-1815, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00428966

C. Amrouche, P. Penel, and N. Seloula, Some Remarks on the Boundary Conditions in the Theory of Navier-Stokes Equations, Annales mathématiques Blaise Pascal, vol.20, issue.1, pp.37-73, 2013.

C. Amrouche and N. E. Seloula, On the Stokes equations with the Navier-type boundary conditions, Differential Equations & Applications, vol.3, issue.4, pp.581-607, 2011.

C. Amrouche and N. E. Seloula, Lp-THEORY FOR VECTOR POTENTIALS AND SOBOLEV'S INEQUALITIES FOR VECTOR FIELDS: APPLICATION TO THE STOKES EQUATIONS WITH PRESSURE BOUNDARY CONDITIONS, Mathematical Models and Methods in Applied Sciences, vol.23, issue.01, pp.37-92, 2012.

H. Beirão-da and . Veiga, Regularity for Stokes and generalized Stokes systems under nonhomogeneous slip-type boundary conditions, Adv. Differential Equations, vol.9, issue.9, pp.1079-1114, 2004.

H. Beirão and . Veiga, On the regularity of flows with Ladyzhenskaya shear-dependent viscosity and slip or nonslip boundary conditions, Comm. Pure Appl. Math, vol.58, issue.4, pp.552-577, 2005.

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.

M. Benjemaa and A. Nasri, A new family of discontinuous finite element methods for elliptic problems in the whole space, Mathematical Methods in the Applied Sciences, vol.42, issue.9, pp.2949-2973, 2019.

L. C.-berselli, An elementary approach to the 3D Navier-Stokes equations with Navier boundary conditions: Existence and uniqueness of various classes of solutions in the flat boundary case., Discrete & Continuous Dynamical Systems - S, vol.3, issue.2, pp.199-219, 2010.

L. C. Berselli and M. Romito, On the Existence and Uniqueness of Weak Solutions for a Vorticity Seeding Model, SIAM Journal on Mathematical Analysis, vol.37, issue.6, pp.1780-1799, 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.
URL : https://hal.archives-ouvertes.fr/hal-02166371

T. Z. Boulmezaoud, Inverted finite elements: a new method for solving elliptic problems in unbounded domains, ESAIM: Mathematical Modelling and Numerical Analysis, vol.39, issue.1, pp.109-145, 2005.

T. Z. Boulmezaoud, K. Kaliche, and N. Kerdid, Inverted finite elements for div-curl systems in the whole space, Advances in Computational Mathematics, vol.43, issue.6, pp.1469-1489, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02169448

T. Z. Boulmezaoud, S. Mziou, and T. Boudjedaa, Numerical Approximation of Second-Order Elliptic Problems in Unbounded Domains, Journal of Scientific Computing, vol.60, issue.2, pp.295-312, 2013.
URL : https://hal.archives-ouvertes.fr/hal-02166382

A. Calderón, Lebesgue spaces of differentiable functions and distributions, Proc. Sympos, vol.IV, pp.33-49, 1961.

M. Cantor, Indiana University Mathematics Journal, vol.24, issue.9, p.897, 1975.

J. Casado-d??az, 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.

P. G. , Mathematical elasticity, volume I: Three-dimensional elasticity, Acta Applicandae Mathematicae, vol.18, issue.2, pp.190-195, 1990.

P. G. Ciarlet and P. G. Ciarlet, ANOTHER APPROACH TO LINEARIZED ELASTICITY AND A NEW PROOF OF KORN'S INEQUALITY, Mathematical Models and Methods in Applied Sciences, vol.15, issue.02, pp.259-271, 2005.

H. Beirao-da-veiga and F. Crispo, Sharp inviscid limit results under Navier slip boundary conditions. an L p theory, J. Math. Fluid Mech, vol.12, issue.4, pp.397-411, 2010.

P. Deuring, Exterior Stationary Navier?Stokes Flows in 3D with Nonzero Velocity at Infinity: Asymptotic Behavior of the Second Derivatives of the Velocity, Communications in Partial Differential Equations, vol.30, issue.7, pp.987-1020, 2005.

R. Farwig, G. P. Galdi, and H. Sohr, Very Weak Solutions of Stationary and Instationary Navier-Stokes Equations with Nonhomogeneous Data, Progress in Nonlinear Differential Equations and Their Applications, vol.64, pp.113-136

R. Farwig, G. P. Galdi, and H. Sohr, A New Class of Weak Solutions of the Navier?Stokes Equations with Nonhomogeneous Data, Journal of Mathematical Fluid Mechanics, vol.8, issue.3, pp.423-444, 2005.

H. Fujita, On the existence and regularity of the steady-state solutions of the Navier-Stokes theorem, J. Fac. Sci. Univ. Tokyo Sect. I, vol.9, pp.59-102, 1961.

G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations, An introduction to the mathematical theory of the Navier-Stokes equations, vol.I, 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.112, issue.4, pp.291-318, 1990.

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, issue.3-4, pp.847-861, 1994.

G. P. Galdi, C. G. Simader, and H. Sohr, A class of solutions to stationary Stokes and Navier-Stokes equations with boundary data in W?1/q,q, Mathematische Annalen, vol.331, issue.1, pp.41-74, 2004.

Y. Giga, Analyticity of the semigroup generated by the Stokes operator inL r spaces, Mathematische Zeitschrift, vol.178, issue.3, pp.297-329, 1981.

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, 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.15, issue.5, pp.345-363, 1992.

V. Girault and P. A. Raviart, Finite Element Methods for Navier-Stokes Equations, 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.114, issue.4, pp.313-333, 1991.

J. Giroire, Étude de quelques problèmes aux limites extérieurs et résolution par équations intégrales, 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.

C. He, The initial boundary value problem for Navier-Stokes equations, Acta Mathematica Sinica, vol.15, issue.2, pp.153-164, 1999.

J. G. Heywood, The Navier-Stokes equations: on the existence, regularity and decay of solutions, Indiana Univ. Math. J, vol.29, issue.5, pp.639-681, 1980.

H. Kim and H. Kozono, On the stationary Navier?Stokes equations in exterior domains, Journal of Mathematical Analysis and Applications, vol.395, issue.2, pp.486-495, 2012.

V. A. Kondrat'ev and O. A. Oleinik, Boundary-value problems for the system of elasticity theory in unbounded domains. Korn's inequalities, Russian Mathematical Surveys, vol.43, issue.5, pp.65-119, 1988.

H. Kozono and H. Sohr, Indiana University Mathematics Journal, vol.40, issue.1, p.1, 1991.

H. Kozono, T. Ogawa, and H. Sohr, Asymptotic behaviour inL r for weak solutions of the Navier-Stokes equations in exterior domains, Manuscripta Mathematica, vol.74, issue.1, pp.253-275, 1992.

L. D. Kudrjavcev, Variational methods for the solution of elliptic equations, Translations of Mathematical Monographs, vol.42, pp.157-202, 1974.

J. Leray, Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique, J. Math. Pures Appl, vol.12, issue.1, pp.1-82, 1933.

J. Leray, Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Mathematica, vol.63, issue.0, pp.193-248, 1934.

A. Liakos, Discretization of the Navier-Stokes equationswith slip boundary condition II, Computers & Mathematics with Applications, vol.48, issue.7-8, pp.1153-1166, 2004.

A. Liakos, Discretization of the Navier-Stokes equations with slip boundary condition, Numerical Methods for Partial Differential Equations, vol.17, issue.1, pp.26-42, 2001.

J. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, 1969.

J. L. Lions and E. Magenes, Problèmes aux limites non homogènes (VI), Journal d'Analyse Mathématique, vol.11, issue.1, pp.165-188, 1963.

H. Louati, M. Meslameni, and U. Razafison, WeightedLp-theory for vector potential operators in three-dimensional exterior domains, Mathematical Methods in the Applied Sciences, vol.39, issue.8, pp.1990-2010, 2015.

H. Louati, M. Meslameni, and U. Razafison, On the three?dimensional stationary exterior Stokes problem with non standard boundary conditions, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, vol.100, issue.6, 2020.
URL : https://hal.archives-ouvertes.fr/hal-02174108

G. Mulone and F. Salemi, On the existence of hydrodynamic motion in a domain with free boundary type conditions, Meccanica, vol.18, issue.3, pp.136-144, 1983.

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.139, issue.1, pp.147-174, 1985.

T. Nakatsuka, On uniqueness of stationary solutions to the Navier?Stokes equations in exterior domains, Nonlinear Analysis: Theory, Methods & Applications, vol.75, issue.8, pp.3457-3464, 2012.

C. L. Navier, Mémoire sur les Lois du Mouvement des fluides, Mem. Acad. Sci. Inst. de France, vol.6, issue.2, pp.389-440, 1827.

C. Parés, Existence, uniqueness and regularity of solution of the equations of a turbulence model for incompressible fluids, Applicable Analysis, vol.43, issue.3-4, pp.245-296, 1992.

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.

J. Serrin, Mathematical Principles of Classical Fluid Mechanics, Encyclopedia of Physics / Handbuch der Physik, pp.125-263, 1959.

V. A. Solonnikov and V. E. Scadilov, Solvability of a three-dimensional boundary value problem with a free surface for the stationary Navier-Stokes system, Banach Center Publications, vol.10, issue.1, pp.361-403, 1983.

M. Specovius-neugebauer and W. Wendland, Exterior stokes problems and decay at infinity, Mathematical Methods in the Applied Sciences, vol.8, issue.1, pp.351-367, 1986.

M. Specovius-neugebauer, Weak solutions of the Stokes problem in weighted Sobolev spaces, Acta Applicandae Mathematicae, vol.37, issue.1-2, pp.195-203, 1994.

M. Specovius-neugebauer, The helmhotz decomposition of weighted lr-Spaces, Communications in Partial Differential Equations, vol.15, issue.3, pp.273-288, 1990.

J. Stam, Real-time fluid dynamics for games, Proceedings of the game developer conference, vol.18, 2003.

R. Temam, Steady-State Navier?Stokes Equations, Navier?Stokes Equations - Theory and Numerical Analysis, vol.2, pp.157-246, 1977.

R. Verfürth, Finite element approximation on incompressible Navier-Stokes equations with slip boundary condition, Numerische Mathematik, vol.50, issue.6, pp.697-721, 1986.

Y. Xiao and Z. Xin, On the vanishing viscosity limit for the 3D Navier-Stokes equations with a slip boundary condition, Communications on Pure and Applied Mathematics, vol.60, issue.7, pp.1027-1055, 2007.