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

Y. Cho and H. Kim, Unique solvability for the density-dependent Navier-Stokes equations, Nonlinear Anal, pp.465-489, 2004.

W. Craig, X. Huang, and Y. Wang, Global Wellposedness for the 3D Inhomogeneous Incompressible Navier?Stokes Equations, Journal of Mathematical Fluid Mechanics, vol.21, issue.1, pp.747-758, 2013.
DOI : 10.1137/0521061

R. Danchin, Local and global well-posedness results for flows of inhomogeneous viscous fluids, Adv. Diff. Eq, vol.9, pp.353-386, 2004.

R. Danchin, Density-Dependent Incompressible Fluids in Bounded Domains, Journal of Mathematical Fluid Mechanics, vol.8, issue.3, pp.333-381, 2006.
DOI : 10.1007/s00021-004-0147-1

R. Danchin and P. B. , Mucha: A Lagrangian Approach for the Incompressible Navier-Stokes Equations with Variable Density, pp.1458-1480, 2012.

R. Danchin and P. B. , Mucha: Divergence, Discrete and Cont, Dyn. Systems S, vol.6, issue.5, pp.1163-1172, 2013.

R. Danchin and P. B. Mucha, Incompressible flows with piecewise constant density, Archive for Rational Mechanics and Analysis, pp.991-1023, 2013.
DOI : 10.1007/s00205-012-0586-4
URL : http://arxiv.org/abs/1203.1131

R. Danchin and P. Zhang, Inhomogeneous Navier?Stokes equations in the half-space, with only bounded density, Journal of Functional Analysis, vol.267, issue.7, pp.2371-2436, 2014.
DOI : 10.1016/j.jfa.2014.07.017
URL : https://hal.archives-ouvertes.fr/hal-00813552

R. Danchin and X. Zhang, On the persistence of Hölder regular patches of density for the inhomogeneous Navier-Stokes equations

B. Desjardins, Global existence results for the incompressible density-dependent Navier-Stokes equations in the whole space, Differential Integral Equations, vol.10, issue.3, pp.587-598, 1997.

B. Desjardins, Regularity of weak solutions of the compressible isentropic navier-stokes equations, Communications in Partial Differential Equations, vol.103, issue.5-6, pp.977-1008, 1997.
DOI : 10.1007/BF01206939

F. Gancedo and E. Garcia-juarez, Global regularity of 2D density patches for inhomogeneous Navier- Stokes

P. Germain, Strong solutions and weak-strong uniqueness for the nonhomogeneous Navier-Stokes system, Journal d'Analyse Math?matique, vol.1, issue.1, pp.169-196, 2008.
DOI : 10.1515/9783110812411

J. Huang, M. Paicu, and P. Zhang, Global Well-posedness of Incompressible Inhomogeneous Fluid Systems with Bounded Density or Non-Lipschitz Velocity, Archive for Rational Mechanics and Analysis, vol.287, issue.4, pp.631-682, 2013.
DOI : 10.1007/s00220-008-0631-1
URL : https://hal.archives-ouvertes.fr/hal-00994718

A. Kazhikhov, Solvability of the initial-boundary value problem for the equations of the motion of an inhomogeneous viscous incompressible fluid, Dokl. Akad. Nauk SSSR, vol.216, pp.1008-1010, 1974.

O. Ladyzhenskaya, Solution ?in the large? of the nonstationary boundary value problem for the Navier-Stokes system with two space variables, Communications on Pure and Applied Mathematics, vol.13, issue.3, pp.427-433, 1959.
DOI : 10.1002/cpa.3160120303

O. Ladyzhenskaya and V. Solonnikov, Unique solvability of an initial- and boundary-value problem for viscous incompressible nonhomogeneous fluids, Journal of Soviet Mathematics, vol.157, issue.5, pp.697-749, 1978.
DOI : 10.1007/BF01085325

J. Leray, Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Mathematica, vol.63, issue.0, pp.193-248, 1934.
DOI : 10.1007/BF02547354

J. Li, Local existence and uniqueness of strong solutions to the Navier-Stokes equations with nonnegative density

X. Liao and P. Zhang, On the Global Regularity of the Two-Dimensional Density Patch for Inhomogeneous Incompressible Viscous Flow, Archive for Rational Mechanics and Analysis, vol.18, issue.9, pp.937-981, 2016.
DOI : 10.1137/0521061

X. Liao and P. Zhang, Global regularities of two-dimensional density patch for inhomogeneous incompressible viscous flow with general density, arXiv:1604.07922. [23] L. Lichtenstein: ¨ Uber einige Existenzprobleme der Hydrodynamik homogenerunzusammendrückbarer, reibungsloser Flüßigkeiten und die Helmoltzochen Wirbelsatze, Mathematische Zeitschrift, vol.23, issue.28, pp.89-154, 1925.

J. Lions and G. Prodi, Un théorème d'existence et unicité dans leséquationsleséquations de Navier-Stokes en dimension 2, Comptes-Rendus de l'Académie des Sciences de Paris, pp.248-3519, 1959.

P. B. Mucha and W. M. Zaj¸aczkowskizaj¸aczkowski, On a Lp-estimate for the linearized compressible Navier?Stokes equations with the Dirichlet boundary conditions, Journal of Differential Equations, vol.186, issue.2, pp.377-393, 2002.
DOI : 10.1016/S0022-0396(02)00017-7

M. Paicu, P. Zhang, and Z. Zhang, Global Unique Solvability of Inhomogeneous Navier-Stokes Equations with Bounded Density, Communications in Partial Differential Equations, vol.3, issue.7, pp.1208-1234, 2013.
DOI : 10.1137/0521061
URL : https://hal.archives-ouvertes.fr/hal-00994640

J. Simon, Nonhomogeneous Viscous Incompressible Fluids: Existence of Velocity, Density, and Pressure, SIAM Journal on Mathematical Analysis, vol.21, issue.5, pp.1093-1117, 1990.
DOI : 10.1137/0521061

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. Danchin and C. Upec, E-mail address: raphael.danchin@u-pec, UPEMLV avenue du Général de Gaulle, pp.61-63