, Inertial effects in the asymptotic behavior of a thin film flow, Asymptotic Anal, pp.177-208, 1994.
, Sobolev spaces, Pure and Applied Mathematics, vol.65, 1975.
, The transition between the Stokes equations and the Reynolds equation: A mathematical proof, Applied Mathematics & Optimization, vol.135, issue.4, pp.73-93, 1986.
DOI : 10.1007/BF01442229
, Asymptotic Navier-Stokes equations in a thin moving boundary domain, Asymptot. Anal, vol.21, issue.2, pp.117-132, 1999.
, Numerical study of viscoelastic mixtures through a Cahn???Hilliard flow model, European Journal of Mechanics - B/Fluids, vol.23, issue.5, pp.759-780, 2004.
DOI : 10.1016/j.euromechflu.2004.03.001
URL : https://hal.archives-ouvertes.fr/hal-00004087
, On the W 2,p -regularity for solutions of mixed problems, J. Math. Pures Appl, vol.9, issue.53, pp.279-290, 1974.
, About a generalized Buckley-Leverett equation and lubrication multifluid flow, European Journal of Applied Mathematics, vol.17, issue.05, pp.491-524, 2006.
DOI : 10.1017/S0956792506006668
URL : https://hal.archives-ouvertes.fr/hal-00383403
, Mathematical study of multi-phase flow under shear through order parameter formulation, Asymptot. Anal, vol.20, issue.2, pp.175-212, 1999.
, Nonhomogeneous Cahn???Hilliard fluids, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.18, issue.2, pp.225-259, 2001.
DOI : 10.1016/S0294-1449(00)00063-9
URL : https://hal.archives-ouvertes.fr/hal-00004085
, A theoretical and numerical model for the study of incompressible mixture flows, Computers and Fluids, pp.41-68, 2002.
, Ecoulement de gouttes dans des microcanaux: simulations numériques et expériences, Proceedings du 18e congrès français de mécanique, 2007.
, Existence result for a mixture of non Newtonian flows with stress diffusion using the Cahn-Hilliard formulation, Discrete Contin, Dyn. Syst. Ser. B, vol.3, issue.1, pp.45-68, 2003.
, Some theoretical results concerning diphasic viscoelastic flows of the Oldroyd kind, Adv. Differential Equations, vol.9, issue.910, pp.1039-1078, 2004.
, Steady state solutions for a lubrication multi-fluid flow, European Journal of Applied Mathematics, vol.59, issue.06, pp.581-612, 2011.
DOI : 10.1023/A:1011509010432
, Elliptic boundary value problems on corner domains, Smoothness and asymptotics of solutions, 1988.
, Dynamics of domains and textures, in Theoretical Challenges in the Dynamics of Complex Fluids, pp.293-314, 1997.
, On the Cahn???Hilliard Equation with Degenerate Mobility, SIAM Journal on Mathematical Analysis, vol.27, issue.2, pp.404-423, 1996.
DOI : 10.1137/S0036141094267662
, Finite element approximation of the Navier- Stokes equations, Lecture Notes in Mathematics, vol.749, 1979.
DOI : 10.1007/BFb0063447
, Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics, vol.24, 1985.
DOI : 10.1137/1.9781611972030
, Lectures on nonlinear hyperbolic differential equations, Mathématiques & Applications, vol.26, 1997.
, Rigorous justification of the Reynolds equations for gas lubrication, C. R. Mécanique, vol.33, issue.7, pp.534-541, 2005.
, Phase transitions of fluids in shear flow, J. Phys. Condens. Matter, issue.9, pp.6119-6157, 1997.
, Asymptotic behavior of a two fluid flow in a thin domain: from Stokes equations to Buckley-Leverett equation and Reynolds law, Asymptot . Anal, vol.34, issue.2, pp.93-120, 2003.
, Compact sets in the space L p p0, T ; Bq, Ann. Mat. Pura Appl, vol.4, issue.146, pp.65-96, 1987.
, Experimental and numerical study of droplets hydrodynamics in microchannels, AIChE Journal, vol.16, issue.80, pp.4061-4070, 2006.
DOI : 10.1002/aic.11033
, Infinite-dimensional dynamical systems in mechanics and physics, Applied Mathematical Sciences, vol.68, 1997.