T. Alazard, Incompressible limit of the nonisentropic Euler equations with solid wall boundary conditions, Adv. Differential Equations, vol.10, issue.1, pp.19-44, 2005.

T. Alazard, Low Mach Number Limit of the Full Navier-Stokes Equations, Archive for Rational Mechanics and Analysis, vol.180, issue.1, pp.1-73, 2006.
DOI : 10.1007/s00205-005-0393-2
URL : https://hal.archives-ouvertes.fr/hal-00153152

S. N. Antontsev, A. V. Kazhikhov, and V. N. Monakhov, Boundary value problems in mechanics of nonhomogeneous fluids, Mathematics and its Applications, 1990.

H. Bahouri, J. Chemin, and R. Danchin, Fourier Analysis and Nonlinear Partial Differential Equations, 2011.
DOI : 10.1007/978-3-642-16830-7
URL : https://hal.archives-ouvertes.fr/hal-00732127

J. Beale, T. Kato, and A. Majda, Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Communications in Mathematical Physics, vol.20, issue.1, pp.61-66, 1984.
DOI : 10.1007/BF01212349

H. Beirão-da-veiga, R. Serapioni, and A. Valli, On the motion of non-homogeneous fluids in the presence of diffusion, Journal of Mathematical Analysis and Applications, vol.85, issue.1, pp.179-191, 1982.
DOI : 10.1016/0022-247X(82)90033-6

J. Bony, Calcul symbolique et propagation des singularit??s pour les ??quations aux d??riv??es partielles non lin??aires, Annales scientifiques de l'??cole normale sup??rieure, vol.14, issue.2, pp.209-246, 1981.
DOI : 10.24033/asens.1404
URL : http://archive.numdam.org/article/ASENS_1981_4_14_2_209_0.pdf

D. Bresch, E. H. Essoufi, and M. Sy, Effect of Density Dependent Viscosities on Multiphasic Incompressible Fluid Models, Journal of Mathematical Fluid Mechanics, vol.9, issue.3, pp.377-397, 2007.
DOI : 10.1007/s00021-005-0204-4

H. Beirão and . Veiga, Diffusion on viscous fluids. Existence and asymptotic properties of solutions, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.10, issue.42, pp.341-355, 1983.

H. Beirão, A. Veiga, and . Valli, Existence of C ? solutions of the Euler equations for nonhomogeneous fluids, Comm. Partial Differential Equations, vol.5, issue.2, pp.95-107, 1980.

H. Beirão, A. Veiga, and . Valli, On the Euler equations for nonhomogeneous fluids, I. Rend. Sem. Mat. Univ. Padova, vol.63, pp.151-168, 1980.

H. Beirão, A. Veiga, and . Valli, On the Euler equations for nonhomogeneous fluids. II, J. Math. Anal. Appl, vol.73, issue.2, pp.338-350, 1980.

R. Danchin, On the well-posedness of the incompressible density-dependent Euler equations in the <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup></mml:math> framework, Journal of Differential Equations, vol.248, issue.8, pp.2130-2170, 2010.
DOI : 10.1016/j.jde.2009.09.007

R. Danchin and F. Fanelli, The well-posedness issue for the density-dependent Euler equations in endpoint Besov spaces, Journal de Math??matiques Pures et Appliqu??es, vol.96, issue.3, pp.253-278, 2011.
DOI : 10.1016/j.matpur.2011.04.005

R. Danchin and X. Liao, ON THE WELL-POSEDNESS OF THE FULL LOW MACH NUMBER LIMIT SYSTEM IN GENERAL CRITICAL BESOV SPACES, Communications in Contemporary Mathematics, vol.14, issue.03, p.1250022, 2012.
DOI : 10.1142/S0219199712500228
URL : https://hal.archives-ouvertes.fr/hal-00664907

D. G. Ebin, The Motion of Slightly Compressible Fluids Viewed as a Motion With Strong Constraining Force, The Annals of Mathematics, vol.105, issue.1, pp.141-200, 1977.
DOI : 10.2307/1971029

D. G. Ebin, Motion of slightly compressible fluids in a bounded domain. I, Communications on Pure and Applied Mathematics, vol.58, issue.4, pp.451-485, 1982.
DOI : 10.1002/cpa.3160350402

D. A. Frank-kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics, 1969.

F. Guillén-gonzález and J. V. Gutiérrez-santacreu, Conditional Stability and Convergence of a Fully Discrete Scheme for Three-Dimensional Navier???Stokes Equations with Mass Diffusion, SIAM Journal on Numerical Analysis, vol.46, issue.5, pp.2276-2308, 2008.
DOI : 10.1137/07067951X

F. Guillén-gonzález and J. V. Gutiérrez-santacreu, Unconditional stability and convergence of fully discrete schemes for $2D$ viscous fluids models with mass diffusion, Mathematics of Computation, vol.77, issue.263, pp.1495-1524, 2008.
DOI : 10.1090/S0025-5718-08-02099-1

T. Hmidi and S. Keraani, Incompressible Viscous Flows in Borderline Besov Spaces, Archive for Rational Mechanics and Analysis, vol.145, issue.5, pp.283-300, 2008.
DOI : 10.1007/s00205-008-0115-7
URL : https://hal.archives-ouvertes.fr/hal-00360590

H. Isozaki, Singular limits for the compressible Euler equation in an exterior domain, Journ??es ??quations aux d??riv??es partielles, vol.381, pp.1-36, 1987.
DOI : 10.5802/jedp.313

H. Isozaki, Singular limits for the compressible Euler equation in an exterior domain. II. Bodies in a uniform flow, Osaka J. Math, vol.26, issue.2, pp.399-410, 1989.

S. Klainerman and A. Majda, Compressible and incompressible fluids, Communications on Pure and Applied Mathematics, vol.33, issue.5, pp.629-651, 1982.
DOI : 10.1002/cpa.3160350503

P. Lions, Mathematical topics in fluid mechanics Incompressible models, of Oxford Lecture Series in Mathematics and its Applications, 1996.

G. Métivier and S. Schochet, The Incompressible Limit of the Non-Isentropic Euler Equations, Archive for Rational Mechanics and Analysis, vol.158, issue.1, pp.61-90, 2001.
DOI : 10.1007/PL00004241

S. Schochet, The compressible Euler equations in a bounded domain: Existence of solutions and the incompressible limit, Communications in Mathematical Physics, vol.8, issue.1, pp.49-75, 1986.
DOI : 10.1007/BF01210792

P. Secchi, On the initial value problem for the equations of motion of viscous incompressible fluids in the presence of diffusion, Boll. Un. Mat. Ital. B, vol.1, issue.63, pp.1117-1130, 1982.

P. Secchi, On the Motion of Viscous Fluids in the Presence of Diffusion, SIAM Journal on Mathematical Analysis, vol.19, issue.1, pp.22-31, 1988.
DOI : 10.1137/0519002

M. Sy, A remark on the Kazhikhov???Smagulov type model: The vanishing initial density, Applied Mathematics Letters, vol.18, issue.12, pp.1351-1358, 2005.
DOI : 10.1016/j.aml.2005.02.030

S. Ukai, The incompressible limit and the initial layer of the compressible Euler equation, Journal of Mathematics of Kyoto University, vol.26, issue.2, pp.323-331, 1986.
DOI : 10.1215/kjm/1250520925

M. Vishik, Hydrodynamics in Besov Spaces, Archive for Rational Mechanics and Analysis, vol.145, issue.3, pp.197-214, 1998.
DOI : 10.1007/s002050050128

W. Wolibner, Un theor???me sur l'existence du mouvement plan d'un fluide parfait, homog???ne, incompressible, pendant un temps infiniment long, Mathematische Zeitschrift, vol.5, issue.1, pp.698-726, 1933.
DOI : 10.1007/BF01474610

R. K. Zeytounian, Theory and applications of viscous fluid flows, 2004.

F. Fanelli, ). Upec, and U. , Avenue du Général De Gaulle F94010 Créteil