]. G. Bibliographie and . Allaire, Analyse numérique et optimisation. Éditions de l'École Polytechnique, 2005.

G. Allaire, Conception optimale de structures, 2006.

D. M. Anderson, G. B. Mc-fadden, and A. A. Wheeler, DIFFUSE-INTERFACE METHODS IN FLUID MECHANICS, Annual Review of Fluid Mechanics, vol.30, issue.1, pp.39-65, 1998.
DOI : 10.1146/annurev.fluid.30.1.139

J. Beaucourt, F. Rioual, T. Séon, T. Biben, and C. Misbah, Steady to unsteady dynamics of a vesicle in a flow, Physical Review E, vol.69, issue.1, p.11906, 2004.
DOI : 10.1103/PhysRevE.69.011906

T. Biben and C. Misbah, Tumbling of vesicles under shear flow within an advected-field approach, Physical Review E, vol.67, issue.3, p.31908, 2003.
DOI : 10.1103/PhysRevE.67.031908

C. Bost, Méthodes Level-Set et pénalisation pour le calcul d'intéractions fluide-structure, 2008.

J. U. Brackbill, D. B. Kothe, and C. Zemach, A continuum method for modeling surface tension, Journal of Computational Physics, vol.100, issue.2, pp.335-354, 1992.
DOI : 10.1016/0021-9991(92)90240-Y

H. Brezis, Analyse fonctionnelle, théorie et applications, Collection Sciences Sup, 1994.

A. Cheng, D. Coutand, and S. Shkoller, Navier???Stokes Equations Interacting with a Nonlinear Elastic Biofluid Shell, SIAM Journal on Mathematical Analysis, vol.39, issue.3, pp.742-800, 2007.
DOI : 10.1137/060656085

A. Chorin, Numerical solution of the Navier-Stokes equations, Mathematics of Computation, vol.22, issue.104, pp.745-762, 1968.
DOI : 10.1090/S0025-5718-1968-0242392-2

P. G. Ciarlet, Mathematical elasticity Vol I, Three dimensional elasticity, Mathematics and its Applications, 1994.

P. G. Ciarlet, Mathematical elasticity Vol II, Theory of plates, Mathematics and its Applications, 1997.

P. G. Ciarlet, Mathematical elasticity Vol III, Theory of shells, Mathematics and its Applications, 2000.

G. Cottet and E. Maitre, A level-set formulation of immersed boundary methods for fluid???structure interaction problems, Comptes Rendus Mathematique, vol.338, issue.7, pp.581-586, 2004.
DOI : 10.1016/j.crma.2004.01.023

G. Cottet and E. Maitre, A LEVEL SET METHOD FOR FLUID-STRUCTURE INTERACTIONS WITH IMMERSED SURFACES, Mathematical Models and Methods in Applied Sciences, vol.16, issue.03, pp.415-438, 2006.
DOI : 10.1142/S0218202506001212

URL : https://hal.archives-ouvertes.fr/hal-00103198

G. Cottet, E. Maitre, and T. Milcent, Eulerian formulation and level set models for incompressible fluid-structure interaction, ESAIM: Mathematical Modelling and Numerical Analysis, vol.42, issue.3, pp.471-492, 2008.
DOI : 10.1051/m2an:2008013

URL : https://hal.archives-ouvertes.fr/hal-00297711

D. Coutand and S. Shkoller, Motion of an Elastic Solid inside an Incompressible Viscous Fluid, Archive for Rational Mechanics and Analysis, vol.52, issue.1, pp.25-102, 2005.
DOI : 10.1007/s00205-004-0340-7

K. Deckelnick, G. Dziuk, and C. M. Elliott, Computation of geometric partial differential equations and mean curvature flow. Acta numerica, pp.139-232, 2005.

M. P. Carmo, Differential geometry of Curves and Surfaces, 1976.

J. Donea, S. Guiliani, and J. P. Halleux, An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interactions, Computer Methods in Applied Mechanics and Engineering, vol.33, issue.1-3, pp.689-723, 1982.
DOI : 10.1016/0045-7825(82)90128-1

G. Duvaut, Mécanique des milieux continus. Dunod, 1998.

L. C. Evans and R. Gariepy, Mesure theory and fine properties of functions, 1992.

M. Fernandez, J. Gerbeau, and C. Grandmont, A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid, International Journal for Numerical Methods in Engineering, vol.9, issue.4, 2005.
DOI : 10.1002/nme.1792

URL : https://hal.archives-ouvertes.fr/hal-00701685

S. Gallot, D. Hulin, and J. Lafontaine, Riemannian geometry, 1982.
URL : https://hal.archives-ouvertes.fr/hal-00002870

C. Galusinski and P. Vigneaux, Level-Set method and stability condition for curvature-driven flows, Comptes Rendus Mathematique, vol.344, issue.11, pp.703-708, 2007.
DOI : 10.1016/j.crma.2007.05.001

URL : https://hal.archives-ouvertes.fr/hal-00193189

C. Grandmont and Y. Maday, Existence for an Unsteady Fluid-Structure Interaction Problem, ESAIM: Mathematical Modelling and Numerical Analysis, vol.34, issue.3, pp.609-636, 2000.
DOI : 10.1051/m2an:2000159

J. Guermond, P. Minev, and J. Shen, An overview of projection methods for incompressible flows, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.44-47, pp.6011-6045, 2006.
DOI : 10.1016/j.cma.2005.10.010

A. Henrot and M. Pierre, Variation et optimisation de formes, une analyse géométrique, Mathématiques et applications Springer no 48, 2005.
DOI : 10.1007/3-540-37689-5

J. Lemoine, On non-homogeneous viscous incompressible fluids. existence of regular solutions, Comment. Math. Univ. Carolinae, vol.38, issue.3, pp.697-715, 1997.

F. Lin, C. Liu, and P. Zhang, On hydrodynamics of viscoelastic fluids, Communications on Pure and Applied Mathematics, vol.39, issue.11, pp.1-35, 2005.
DOI : 10.1002/cpa.20074

P. Lions, Mathematical topics in fluid mechanics volume 1 : incompressible models. Oxford lecture series in mathematics and its applications, 1996.

X. Liu, S. Osher, and T. Chan, Weighted Essentially Non-oscillatory Schemes, Journal of Computational Physics, vol.115, issue.1, pp.200-212, 1994.
DOI : 10.1006/jcph.1994.1187

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

E. Maitre, T. Milcent, G. Cottet, A. Raoult, and Y. Usson, Applications of level set methods in computational biophysics, Mathematical and Computer Modelling, vol.49, issue.11-12, 2008.
DOI : 10.1016/j.mcm.2008.07.026

URL : https://hal.archives-ouvertes.fr/hal-00177593

A. J. Majda and A. L. Bertozzi, Vorticity and Incompressible Flow. Cambridge Texts in Applied Mathematics, Applied Mechanics Reviews, vol.55, issue.4, 2002.
DOI : 10.1115/1.1483363

B. Maury and O. Pironneau, Characteristics ale method for unsteady free surface flows with surface tension, Z. Angew. Math. Mech. (ZAMM), vol.76, issue.2, pp.613-614, 1996.

A. Miranville and R. Temam, Modélisation mathématique et mécanique des milieux continus, 2003.

C. Misbah, Vacillating Breathing and Tumbling of Vesicles under Shear Flow, Physical Review Letters, vol.96, issue.2, p.28104, 2006.
DOI : 10.1103/PhysRevLett.96.028104

S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Applied Mechanics Reviews, vol.57, issue.3, 2003.
DOI : 10.1115/1.1760520

URL : http://dx.doi.org/10.1016/s0898-1221(03)90179-9

S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988.
DOI : 10.1016/0021-9991(88)90002-2

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

C. S. Peskin, The immersed boundary method, Acta Numerica, pp.1-39

J. A. Sethian, P. Smereka, and S. Osher, A level set approach for computing solutions to incompressible two-phase flow, J. Comp. Phys, vol.114, pp.146-159, 1994.

J. Simon, Compact sets in the spaceL p (O,T; B), Annali di Matematica Pura ed Applicata, vol.287, issue.1, pp.65-96, 1987.
DOI : 10.1007/BF01762360

J. Simon, Différentiation de problèmes aux limites par rapport au domaine, 1991.

V. A. Solonnikov, Estimates for solutions of nonstationary Navier-Stokes equations, Journal of Soviet Mathematics, vol.70, issue.No. 4, pp.467-529, 1977.
DOI : 10.1007/BF01084616

D. Steigmann, E. Baesu, E. Rudd, and J. Belak, On the variational theory of cell-membrane equilibria . Interfaces and Free Boundaries, pp.357-366, 2003.

M. Sy, D. Bresch, F. Guillen-gonzalez, J. Lemoine, and M. A. Rodriguez-bellido, Local strong solution for the incompressible Korteweg model, Comptes Rendus Mathematique, vol.342, issue.3, pp.169-174, 2006.
DOI : 10.1016/j.crma.2005.12.003

URL : https://hal.archives-ouvertes.fr/hal-00103202

R. Temam, Une m??thode d'approximation de la solution des ??quations de Navier-Stokes, Bulletin de la Société mathématique de France, vol.79, pp.115-152, 1968.
DOI : 10.24033/bsmf.1662

A. K. Tornberg and B. Engquist, Numerical approximations of singular source terms in differential equations, Journal of Computational Physics, vol.200, issue.2, pp.462-488, 2004.
DOI : 10.1016/j.jcp.2004.04.011

M. Tucsnack, J. San-martin, and V. Starovoitov, Global weak solutions for the two dimensional motion of several rigid bodies in an incompressible viscous fluid. Archive for Rational Mechanics and Analysis, pp.113-147, 2002.

T. J. Willmore, Total curvature in riemannian geometry, Ellis Horwood Series Mathematics and its applications, 1982.

S. Xu and Z. J. Wang, Systematic Derivation of Jump Conditions for the Immersed Interface Method in Three-Dimensional Flow Simulation, SIAM Journal on Scientific Computing, vol.27, issue.6, pp.1948-1980, 2006.
DOI : 10.1137/040604960