Danchin: Fourier Analysis and Nonlinear Partial Differential Equations, p.343, 2011. ,
A GENERAL WAVELET-BASED PROFILE DECOMPOSITION IN THE CRITICAL EMBEDDING OF FUNCTION SPACES, Confluentes Mathematici, vol.03, issue.03, pp.1-25, 2011. ,
DOI : 10.1142/S1793744211000370
On the stability in weak topology of the set of global solutions to the Navier-Stokes equations, Archive for Rational Mechanics and Analysis, pp.569-629, 2013. ,
High Frequency Approximation of Solutions to Critical Nonlinear Wave Equations, American Journal of Mathematics, vol.121, issue.1, pp.131-175, 1999. ,
DOI : 10.1353/ajm.1999.0001
Lack of compactness in the 2D critical Sobolev embedding, the general case ,
URL : https://hal.archives-ouvertes.fr/hal-00796004
Refinements of Strichartz' inequality and applications to 2 D-NLS with critical nonlinearity, Internatinal Mathematical Research Notices, vol.5, pp.253-283, 1998. ,
Ill-posedness of the Navier???Stokes equations in a critical space in 3D, Journal of Functional Analysis, vol.255, issue.9, pp.2233-2247, 2008. ,
DOI : 10.1016/j.jfa.2008.07.008
Coron: Convergence of solutions of H-Systems or how to blow bubbles, Archive for Rational Mechanics and Analysis, pp.21-86, 1985. ,
Partial regularity of suitable weak solutions of the navier-stokes equations, Communications on Pure and Applied Mathematics, vol.8, issue.6, pp.771-831, 1982. ,
DOI : 10.1002/cpa.3160350604
A generalization of a theorem by Kato on Navier-Stokes equations, Revista Matem??tica Iberoamericana, vol.13, issue.3, pp.515-541, 1997. ,
DOI : 10.4171/RMI/229
Solutions auto-similaires des équations de Navier-Stokes, Séminaire Equations aux Dérivées Partielles de l'Ecole Polytechnique, 1993. ,
Large, global solutions to the Navier-Stokes equations, slowly varying in one direction, Transactions of the, pp.2859-2873, 2010. ,
Wellposedness and stability results for the Navier???Stokes equations in <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>R</mml:mi><mml:mn>3</mml:mn></mml:msup></mml:math>, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.26, issue.2, pp.599-624, 2009. ,
DOI : 10.1016/j.anihpc.2007.05.008
Flow of Non-Lipschitz Vector-Fields and Navier-Stokes Equations, Journal of Differential Equations, vol.121, issue.2, pp.314-328, 1995. ,
DOI : 10.1006/jdeq.1995.1131
Self-improving bounds for the Navier-Stokes equations, Bulletin de la Société mathématique de France, vol.140, issue.4, pp.2012-583, 2013. ,
DOI : 10.24033/bsmf.2638
URL : https://hal.archives-ouvertes.fr/hal-00936366
-solutions of the Navier-Stokes equations and backward uniqueness, Russian Mathematical Surveys, vol.58, issue.2, pp.3-44, 2003. ,
DOI : 10.1070/RM2003v058n02ABEH000609
URL : https://hal.archives-ouvertes.fr/hal-00908918
On the Navier-Stokes initial value problem I, Archive for Rational Mechanics and Analysis, pp.269-315, 1964. ,
Profile decomposition for solutions of the Navier-Stokes equations, Bulletin de la Société mathématique de France, vol.129, issue.2, pp.285-316, 2001. ,
DOI : 10.24033/bsmf.2398
Asymptotics and stability for global solutions to the Navier-Stokes equations, Annales de l'Institut Fourier, pp.1387-1424, 2003. ,
A profile decomposition approach to the $$L^\infty _t(L^{3}_x)$$ Navier???Stokes regularity criterion, Mathematische Annalen, vol.260, issue.3, pp.1527-1559, 2013. ,
DOI : 10.1007/s00208-012-0830-0
URL : https://hal.archives-ouvertes.fr/hal-00936368
Planchon: Blow-up of critical Besov norms at a Navier-Stokes singularity, to appear, Communications in Mathematical Physics, 2015. ,
Description du défaut de compacité de l'injection de Sobolev, ESAIM Contrôle Optimal et Calcul des Variations, pp.213-233, 1998. ,
Microlocal defect measures, Communications in Partial Differential Equations, vol.114, issue.11, pp.1761-1794, 1991. ,
DOI : 10.1080/03605308508820384
The second iterate for the Navier???Stokes equation, Journal of Functional Analysis, vol.255, issue.9, pp.2248-2264, 2008. ,
DOI : 10.1016/j.jfa.2008.07.014
Analysis of the Lack of Compactness in the Critical Sobolev Embeddings, Journal of Functional Analysis, vol.161, issue.2, pp.384-396, 1999. ,
DOI : 10.1006/jfan.1998.3364
Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions, Inventiones mathematicae, vol.312, issue.3, pp.233-265, 2014. ,
DOI : 10.1007/s00222-013-0468-x
StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions, Mathematische Zeitschrift, vol.74, issue.4, pp.471-480, 1984. ,
DOI : 10.1007/BF01174182
An alternative approach to regularity for the Navier???Stokes equations in critical spaces, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.28, issue.2, 2010. ,
DOI : 10.1016/j.anihpc.2010.10.004
Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation, Acta Mathematica, vol.201, issue.2, pp.147-212, 2008. ,
DOI : 10.1007/s11511-008-0031-6
URL : https://hal.archives-ouvertes.fr/hal-00174402
Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schr??dinger equation in the radial case, Inventiones mathematicae, vol.48, issue.2, pp.645-675, 2006. ,
DOI : 10.1007/s00222-006-0011-4
On the Defect of Compactness for the Strichartz Estimates of the Schr??dinger Equations, Journal of Differential Equations, vol.175, issue.2, pp.353-392, 2001. ,
DOI : 10.1006/jdeq.2000.3951
Profile decompositions for critical Lebesgue and Besov space embeddings, Indiana University Mathematics Journal, vol.59, issue.5, pp.1801-1830, 2010. ,
DOI : 10.1512/iumj.2010.59.4426
Well-posedness for the Navier???Stokes Equations, Advances in Mathematics, vol.157, issue.1, pp.22-35, 2001. ,
DOI : 10.1006/aima.2000.1937
On Lerays self-similar solutions of the Navier-Stokes equations, Acta Mathematica, vol.176, issue.2, pp.283-294, 1996. ,
Recent Developments in the Navier-Stokes Problem, Chapman & Hall/CRC Res. Notes Math, vol.431, pp.148-151, 2002. ,
DOI : 10.1201/9781420035674
Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Mathematica, vol.63, issue.0, pp.193-248, 1933. ,
DOI : 10.1007/BF02547354
The concentration-compactness principle in the calculus of variations. The limit case I, Revista. Matematica Iberoamericana, vol.1, issue.1, pp.145-201, 1985. ,
The concentration-compactness principle in the calculus of variations. The limit case II, Revista. Matematica Iberoamericana, vol.1, issue.2, pp.45-121, 1985. ,
Compactness at blow-up time for L 2 solutions of the critical nonlinear Schrödinger equation in 2D, International Mathematical Research Notices, pp.399-425, 1998. ,
Wavelets, paraproducts, and Navier-Stokes equations, Current developments in mathematics, pp.105-212, 1996. ,
The Navier???Stokes Equations in Nonendpoint Borderline Lorentz Spaces, Journal of Mathematical Fluid Mechanics, vol.69, issue.4, 2014. ,
DOI : 10.1007/s00021-015-0229-2
Asymptotic behavior of global solutions to the Navier-Stokes equations in IR 3, Revista Matemática Iberoamericana, vol.14, issue.1, pp.71-93, 1998. ,
About the behaviour of regular Navier-Stokes solutions near the blow up, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01010898
Minimal initial data for potential Navier???Stokes singularities, Journal of Functional Analysis, vol.260, issue.3, pp.879-891, 2011. ,
DOI : 10.1016/j.jfa.2010.09.009
Synopsis, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.1, issue.3-4, pp.193-2301, 1990. ,
DOI : 10.1007/BFb0063632
Equation de Navier-Stokes avec densit?? et viscosit?? variables dans l???espace critique, Revista Matem??tica Iberoamericana, vol.23, issue.2, pp.537-586, 2007. ,
DOI : 10.4171/RMI/505
Global existence for an nonhomogeneous fluid, Annales de l???institut Fourier, vol.57, issue.3, pp.883-917, 2007. ,
DOI : 10.5802/aif.2280
On the decay and stability of global solutions to the 3-D inhomogeneous Navier-Stokes equations, Communications on Pure and Applied Mathematics, vol.35, issue.6, pp.832-881, 2011. ,
DOI : 10.1002/cpa.20351
On the wellposedness of 3-D inhomogeneous Navier-Stokes equations in the critical spaces, Arch. Ration. Mech. Anal, vol.204, pp.2012-189 ,
Danchin: Fourier Analysis and Nonlinear Partial Differential Equations, p.343, 2011. ,
DOI : 10.1007/978-3-642-16830-7
Density-dependent incompressible viscous fluids in critical spaces, Proc. Roy. Soc. Edinburgh Sect.A, 133, pp.1311-1334, 2003. ,
DOI : 10.1017/S030821050000295X
Local and global well-posedness results for flows of inhomogeneous viscous fluids, Adv. Differential Equations, vol.9, pp.353-386, 2004. ,
A Lagrangian Approach for the Incompressible Navier-Stokes Equations with Variable Density, Communications on Pure and Applied Mathematics, vol.51, issue.5, pp.1458-1480, 2012. ,
DOI : 10.1002/cpa.21409
URL : https://hal.archives-ouvertes.fr/hal-00795409
Incompressible Flows with Piecewise Constant Density, Archive for Rational Mechanics and Analysis, vol.51, issue.5 ,
DOI : 10.1007/s00205-012-0586-4
URL : https://hal.archives-ouvertes.fr/hal-00676603
On the Navier-Stokes initial value problem I, Archive for Rational Mechanics and Analysis, pp.269-315, 1964. ,
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 : 10.1007/s11854-008-0034-4
Solvability of the initial-boundary value problem for the equations of the motion of an inhomogeneous viscous incompressible fluid, Russian) Dokl. Akad. Nauk SSSR, vol.216, pp.1008-1010, 1974. ,
The unique solvability of an initial-boundary value problem for viscous incompressible inhomogeneous fluids. (Russian) Boundary value problems of mathematical physics, and related questions of the theory of functions, Zap. Naucn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), vol.8, issue.52, pp.52-109, 1975. ,
Recent Developments in the Navier-Stokes Problem, Chapman & Hall/CRC Res. Notes Math, vol.431, pp.148-151, 2002. ,
DOI : 10.1201/9781420035674
Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Mathematica, vol.63, issue.0, pp.193-248, 1933. ,
DOI : 10.1007/BF02547354
Global solutions to the 3-D incompressible inhomogeneous Navier???Stokes system, Journal of Functional Analysis, vol.262, issue.8, pp.3556-3584, 2012. ,
DOI : 10.1016/j.jfa.2012.01.022
URL : https://hal.archives-ouvertes.fr/hal-00994719
Global Unique Solvability of Inhomogeneous Navier-Stokes Equations with Bounded Density, Communications in Partial Differential Equations, vol.3, issue.7, pp.2013-1208 ,
DOI : 10.1137/0521061
URL : https://hal.archives-ouvertes.fr/hal-00994640
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