M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, 1980.

J. H. Albert, Genericity of simple eigenvalues for elliptic pde's, Proc. Amer. Math. Soc, vol.48, pp.413-418, 1975.

J. H. Albert, Topology of the nodal and critical point sets for eigenfunctions of elliptic operators, M. I. T, 1971.

H. Ammari, An introduction to Mathematics of Emerging Biomedical Imaging, vol.62, 2008.

H. Ammari, E. Beretta, E. Francini, H. Kang, and M. Lim, Reconstruction of small interface changes of an inclusion from modal measurements II: The elastic case, Journal de Mathématiques Pures et Appliquées, vol.94, pp.322-339, 2010.

H. Ammari, P. Garapon, H. Kang, and H. Lee, A method of biological tissues elasticity reconstruction using magnetic resonance elastography measurements, Quarterly of Applied Mathematics, vol.66, issue.1, pp.139-175, 2008.

H. Ammari, P. Garapon, H. Kang, and L. H. , Effective viscosity properties of dilute suspensions of arbitrarily shaped particles, Asymptotic Analysis, vol.80, pp.189-211, 2012.

H. Ammari, H. Kang, and H. Lee, Layer Potential Techniques in Spectral Analysis, Mathematical Surveys and Monographs, vol.153, 2009.

H. Ammari, H. Kang, M. Lim, and H. Zribi, Conductivity interface problems. Part I: Small perturbation of an interface, Trans. Amer. Math. Soc, vol.362, pp.2435-2449, 2010.

H. Ammari and F. Triki, Splitting of resonant and scattering frequencies under shape deformation, J. Differ. Equations, vol.202, issue.2, pp.231-255, 2004.

M. S. Ashbaugh, On universal inequalities for the low eigenvalues of the buckling problem, Partial differential equations and inverse problems, vol.362, pp.13-31, 2004.

I. Babuska, J. E. Osborn, and E. Problems, Handbook of Numerical Analysis, vol.II, pp.641-787, 1991.

I. Balloumi, C. Daveau, and A. Abdennadher, Asymptotic expansion of the solution of the transmission Stokes system with a small boundary perturbation for an inclusion, Complex variables and elliptic euquations, 2018.

F. Boyer and P. Fabrie, Mathematical tools for the study of the incompressible Navier-Stokes equations and related models, Applied Mathematical Sciences, vol.183, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00777731

W. Borchers and W. Varnhorn, On the boundedness of the Stokes semigroup in twodimensional exterior domains, Math. Z, vol.213, issue.2, pp.275-299

C. Daveau, A. Khelifi, and I. Balloumi, Asymptotic Behaviors for Eigenvalues and Eigenfunctions Associated to Stokes Operator in the Presence of Small Boundary Perturbations, Math Phys Anal Geom, vol.20, issue.2, 2017.

N. Depauw, Solutions des équations de Navier Stokes incompressibles dans un domaine exterieur, Rev. Mat. Iberoam, vol.17, pp.21-68, 2001.

L. Escauriaza, E. Fabes, and G. Verchota, On a regularity theorem for weak solutions to transmission problems with internal Lipschitz boundaries, Proc. Amer. Math. Soc, vol.115, pp.1069-1076, 1992.

L. Escauriaza and M. Mitrea, Transmission problems and spectral theory for singular integral operators on Lipschitz domains, J. Funct. Anal, vol.216, pp.141-171, 2004.

L. Escauriaza and J. K. Seo, Regularity properties of solutions to transmission problems, Trans. Amer. Math. Soc, vol.338, pp.405-430, 1993.

E. Fabes, H. Kang, and J. K. Seo, Inverse conductivity problem with one measurement: Error estimates and approximate identification for perturbed disks, SIAM J. MATH. ANAL, vol.30, issue.4, pp.699-720, 1999.

R. Farwig and H. Sohr, An approach to resolvent estimates for the Stokes equations in Lq-spaces, Lecture Notes in Mathematics, vol.1530, pp.97-110, 1990.

G. P. Galdi, An introduction to the Mathematical Theory of the Navier-Stokes equations, Steady-State problem, 2011.

D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, 1983.

D. Givoli, Numerical methods for problems in infinite domains, 1992.

E. J. Hinch, Perturbation methods, 1991.

G. C. Hsiao and W. L. Wendland, Boundary Integral Equations Variational Methods, 2008.

J. P. Kelliher, Eigenvalues of the Stokes operator versus the Dirichlet Laplacian in the plane, Pac. J. Math, vol.244, issue.1, pp.99-132, 2010.

T. Kato, Perturbation Theory for Linear Operators, 1980.

A. Khelifi, Asymptotic property and convergence estimation for the eigenelements of the Laplace operator, Appl. Anal, vol.86, issue.10, pp.1249-1264, 2007.

A. Khelifi and H. Zribi, Boundary voltage perturbations resulting from small surface changes of a conductivity inclusion, Appl. Anal, vol.93, issue.1, pp.46-64, 2014.

M. Kohr, A mixed boundary value problem for the unsteady Stokes system in a bounded domain in Rn, Math. Nachr, vol.280, issue.6, pp.534-559, 2007.

M. Kohr, An indirect boundary integral method for an oscillatory Stokes flow problem, IJMMS, vol.47, pp.2916-2976, 2003.

M. Kohr, The interior Neumann problem for the Stokes resolvent system in a bounded domain in R n, Arch. Mech, vol.59, pp.283-304, 2007.

M. Kohr, C. Pintea, and W. L. Wendland, Stokes-Brinkman transmission problems on Lipschitz and C 1 domains in Riemannian manifolds, Commun. Pure Appl. Anal, vol.9, pp.493-537, 2010.

R. Kress, Linear Integral Equations, vol.82, 1999.

O. A. Ladyzhenskaya, Mathematical theory of the viscous incompressible id. Fizmathiz, p.203, 1961.

V. Lange, Equations intégrales espace-temps pour les équations de Maxwell : calcul du champ diffracté par un obstacle dissipatif, 1995.

M. Lenoir, Influence coefficients for variational integral equations, Comptes Rendus Mathematique, vol.343, pp.561-564, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00876238

M. Lenoir and N. Salles, Evaluation of 3-d singular and nearly singular integrals in Galerkin BEM for thin layers, SIAM Journal on Scientific Computing, vol.34, issue.6, pp.3057-3078, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00969175

Y. Y. Li and L. Nirenberg, Estimates for elliptic systems from composite material, Comm. Pure Appl. Math, vol.56, pp.892-925, 2003.

T. H. Luong and C. Daveau, Asymptotic formula for the solution of the Stokes problem with a small perturbation of the domain in two and three dimensions, Complex Variables and Elliptic Equations, vol.59, pp.1269-1282, 2015.

M. Mccracken, The resolvent problem for the Stokes equations on halfspaces in Lp, SIAM J. Math. Anal, vol.12, pp.201-228, 1981.

Y. Meyer, R. Coifman, M. Wavelet-calderón-zygmund, and . Operators, , 1997.

D. Medková, Integral representation of a solution of the Neumann problem for the Stokes system, Kragujivac J. Math, vol.39, pp.53-71, 2015.

D. Medkova and W. Varnhorn, Boundary value problems for the Stokes equations with jumps in open sets, Applicable Analysis, vol.87, issue.7, pp.829-849, 2008.

M. Mitrea and M. Wright, Boundary Value Problems for the Stokes system in arbitrary Lipschitz domains, Astérisque, vol.344, 2012.

J. C. Nédélec, Acoustic and electromagnetic equations: Integral representation for harmonic problems, vol.144, 2000.

J. H. Ortega and E. Zuazua, Generic simplicity of the eigenvalues of the stokes system in two space dimensions, Advances in Differential Equations, vol.6, issue.8, pp.987-1023, 2001.

J. Osborn, Spectral approximation for compact operators, Math. of Comp, vol.29, pp.712-725, 1975.

Y. Rahmat-samii and J. Daniel, Hoppe Impedance Boundary Conditions in Electromagnetics, 1995.

T. B. Senior and J. L. Volakis, Approximate boundary conditions in electromagnetics, IEE Electromagnetic Waves Series, vol.41, 1995.

R. Temam, Navier-Stokes equations theory and numerical analysis, 1977.

R. Temam, Theory and numerical analysis, 1984.

T. F. Banchoff and S. T. Ovett, Differential geometry of curves and surfaces, LLC, 2010.

M. Van-dyke, Perturbation methods in fluids mechanics, 1975.

W. Varhorn, An explicit potential theory for the Stokes resolvent boundary value problems in three dimensions, Manuscripta Math, vol.70, issue.4, pp.339-361, 1991.

W. Varnhorn, Boundary value problems and integral equations for the Stokes resolvent in bounded and exterior domains of R 3 , Theory of the Navier-Stokes Equations

G. Heywood, K. Masuda, R. Rautmann, and V. A. Solonnikov, World Sci. Publ, pp.206-224, 1998.

W. Varnhorn, The boundary value problems of the Stokes resolvent equations in n dimensions, Math. Nachr. 269, vol.270, pp.210-230, 2004.

W. Varnhorn, The Stokes equations, 1994.

G. C. Verchota, Layer potentials and regularity for Laplace's equation in Lipschitz domains, J. Funct. Anal, vol.59, pp.572-611, 1984.

H. Zribi, Asymptotic expansions for currents caused by a small interface changes of an electromagnetic nclusion, Appl. Anal, vol.92, pp.172-190, 2009.

. Jia, . Shanghu, . Xie, Y. Hehu, . Xiaobo et al., Approximation and eigenvalue extrapolation of Stokes eigenvalue problem by nonconforming finite element methods, Applications of Mathematics, vol.54, issue.1, pp.1-15, 2009.