Espaces critiques pour le système deséquationsdeséquations de Navier- Stokes incompressibles. ArXiv e-prints, arXiv 0812, p.1158, 2008. ,
Gevrey regularity for a class of dissipative equations with applications to decay, Journal of Differential Equations, vol.253, issue.10, pp.2739-2764, 2012. ,
DOI : 10.1016/j.jde.2012.08.003
Existence and stability of steady-state solutions with finite energy for the Navier???Stokes equation in the whole space, Nonlinearity, vol.22, issue.7, pp.1615-1637, 2009. ,
DOI : 10.1088/0951-7715/22/7/007
-Solutions of the Steady-State Navier???Stokes Equations with Rough External Forces, Communications in Partial Differential Equations, vol.11, issue.2, pp.216-246, 2010. ,
DOI : 10.1007/978-1-4612-1015-3
Essai sur la théorie des eaux courantes. Mémoires présentés par divers savantsà savantsà l, Académie des Sciences, vol.23, issue.1, pp.1-660, 1877. ,
´ Elements d'analyse pour l'´ etude de quelques modèles d'´ ecoulements de fluides visqueux incompressibles, 2000. ,
IntroductionàIntroductionà la turbulence, 2013. ,
URL : https://hal.archives-ouvertes.fr/cel-01228137
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 : 10.1090/trans2/065/03
Ondelettes, paraproduits et Navier?Stokes, 1995. ,
Mathematical and Numerical Foundations of Turbulence Models and Applications. Modeling and Simulation in Science, Engineering and Technology, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01149312
Liouville-Type Theorems for the Forced Euler Equations and the Navier???Stokes Equations, Communications in Mathematical Physics, vol.143, issue.1, pp.37-48, 2014. ,
DOI : 10.1007/s002050050099
Frequency decay for Navier-Stokes stationary solutions, Preprint. C. R. Acad. Sci, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01664935
An inviscid dyadic model of turbulence: The global attractor, Discrete and Continuous Dynamical Systems, vol.26, issue.3, pp.781-794, 2010. ,
DOI : 10.3934/dcds.2010.26.781
Bounds on dissipation for Navier???Stokes flow with Kolmogorov forcing, Physica D: Nonlinear Phenomena, vol.158, issue.1-4, pp.105-128, 2001. ,
DOI : 10.1016/S0167-2789(01)00320-7
Analyse combinatoire -Tome premier. Collection Sup -Le mathématicien, 1970. ,
Euler equations Navier-Stokes equations and turbulence, Mathematical Foundation of Turbulent Viscous Flows, of the series Lecture Notes in Mathematics, pp.1-43, 2005. ,
Navier-Stokes Equations, 1988. ,
Inviscid Limit for Damped and Driven Incompressible Navier-Stokes Equations in $$\mathbb R^2$$, Communications in Mathematical Physics, vol.157, issue.4, pp.529-551, 2007. ,
DOI : 10.4310/CMS.2004.v2.n3.a4
Bounds for second order structure functions and energy spectrum in turbulence, Physics of Fluids, vol.12, issue.8, 1999. ,
DOI : 10.1063/1.858329
On Energy Cascades in the Forced 3D Navier???Stokes Equations, Journal of Nonlinear Science, vol.244, issue.2, pp.683-715, 2016. ,
DOI : 10.1007/s00220-003-0974-6
On the steady-state solutions of the navier-stokes equations, III, Acta Mathematica, vol.105, issue.3-4, pp.197-244, 1961. ,
DOI : 10.1007/BF02559590
Energy dissipation in body-forced turbulence, Journal of Fluid Mechanics, vol.467, pp.289-306, 2002. ,
DOI : 10.1017/S0022112002001386
Bounds for the mean dissipation of 2-D enstrophy and 3-D energy in turbulent flows, Physics Letters A, vol.174, issue.3, pp.210-215, 1993. ,
DOI : 10.1016/0375-9601(93)90760-W
Estimates for the energy cascade in three-dimensional turbulent flows, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.333, issue.5, pp.509-514, 2001. ,
DOI : 10.1016/S0764-4442(01)02008-0
Kolmogorov theory via finite-time averages, Physica D: Nonlinear Phenomena, vol.212, issue.3-4, pp.245-270, 2005. ,
DOI : 10.1016/j.physd.2005.10.002
Navier-Stokes Equations and Turbulence, Encyclopedia of Mathematics and its Applications, 2001. ,
Gevrey class regularity for the solutions of the Navier-Stokes equations, Journal of Functional Analysis, vol.87, issue.2, pp.359-369, 1989. ,
DOI : 10.1016/0022-1236(89)90015-3
On the Navier-Stokes initial value problem. I, Archive for Rational Mechanics and Analysis, vol.128, issue.4, pp.269-315, 1964. ,
DOI : 10.1017/S0027763000002415
An introduction to the mathematical Theory of the Navier-Stokes equations : Steady-state problems, 1994. ,
Inégalités de Sobolev précisées. Séminairé Equations aux dérivées partielles, 1996. ,
Sur la nature analytique des solutions deséquationsdeséquations aux dérivées partielles. Premier mémoire. Annales scientifiques de l' ´ Ecole Normale Supérieure, Série, vol.3, issue.35, pp.129-190, 1918. ,
Modern Fourier Analysis, 2009. ,
Space analyticity for the Navier?Stokes and related equations with initial data in Lp, J. Funct. Anal, vol.152, pp.247-466, 1998. ,
Estimations du taux de dissipation d'´ energie cinétique turbulente, Projet de recherche en laboratoire MEC559-MEC569, ´ Ecole Polytechnique, 2004. ,
The Damped-Driven 2D Navier???Stokes System on Large Elongated Domains, Journal of Mathematical Fluid Mechanics, vol.10, issue.2, pp.159-175, 2008. ,
DOI : 10.1007/s00021-006-0226-6
Upper bounds for the attractor simension of damped Navier- Stokes equations in R 2 . Discrete and continous dynamical systems, pp.2085-2102, 2016. ,
, Turbulence et Tourbullons. Majeure, vol.1, 2006.
, , 1998.
Gevrey Regularity for the Attractor of the 3D Navier???Stokes???Voight Equations, Journal of Nonlinear Science, vol.96, issue.1, pp.133-149, 2009. ,
DOI : 10.1007/978-1-4684-0313-8
Energy and spectral dynamics in decaying compressible turbulence, Journal of Scientific Computing, vol.2, issue.1, pp.1-34, 1992. ,
DOI : 10.1063/1.857767
The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.434, issue.1890, p.30, 1941. ,
DOI : 10.1098/rspa.1991.0075
On Degeneration of Isotropic turbulence in an incompressible viscous liquid, Dokl. Akad. Nauk SSSR, p.31, 1941. ,
Dissipation of Energy in the Locally Isotropic Turbulence, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.434, issue.1890, 1941. ,
DOI : 10.1098/rspa.1991.0076
Bounds on Energy and Helicity Dissipation Rates of Approximate Deconvolution Models of Turbulence, SIAM Journal on Mathematical Analysis, vol.39, issue.3, pp.916-931, 2007. ,
DOI : 10.1137/06066223X
Recent developments in the Navier-Stokes problem, 2002. ,
DOI : 10.1201/9781420035674
The Navier-Stokes Problem in the 21st Century, 2016. ,
DOI : 10.1201/b19556
Une remarque sur l'analyticit?? des solutions milds des ??quations de Navier???Stokes dans, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.330, issue.3, pp.183-186, 2000. ,
DOI : 10.1016/S0764-4442(00)00103-8
The study of Navier-Stokes equations for stationnary motion of an imcompressible liquid, Usp. Mat. Nawk, vol.15, pp.75-97, 1959. ,
The mathematical theory of viscous incompressible flow ; Gordon and Breach, 1963. ,
Stochastic cascades and 3-dimensional Navier-Stokes equations, Probab. Theory Related Fields, pp.343-366, 1997. ,
Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Mathematica, vol.63, issue.0, pp.193-248, 1934. ,
DOI : 10.1007/BF02547354
Long-time turbulence model deduced from the Navier-Stokes equations, Chinese Annals of Mathematics, Series B, vol.151, issue.5???6, pp.883-894, 2015. ,
DOI : 10.1098/rspa.1935.0158
URL : https://hal.archives-ouvertes.fr/hal-01192773
Introductory lectures on turbulence : Physics, Mathematics and Modeling, Departments of Mechanical Engineering and Mathematics, 2004. ,
Energy spectrum in the dissipation range of fluid turbulence, Journal of Plasma Physics, vol.57, issue.1, pp.195-201, 1996. ,
DOI : 10.1017/S0022377896005338
On the energy spectrum for weak solutions of the Navier???Stokes equations, Nonlinearity, vol.18, issue.1, p.18, 2004. ,
DOI : 10.1088/0951-7715/18/1/001
Ondelettes et Opérateurs, Tome 1. Hermann, ´ Editeurs des sciences et des arts, 1990. ,
On the energy distribution in the spectrum of a turbulent flow, Dokl. Akad. Nauk SSSR, p.32, 1941. ,
Spatial smoothness of the stationary solutions of the 3D Navier?Stokes equations . arXiv :math, 512057. ,
URL : https://hal.archives-ouvertes.fr/hal-00015081
Remark on the Rate of Decay of Higher Order Derivatives for Solutions to the Navier???Stokes Equations in Rn, Journal of Functional Analysis, vol.172, issue.1, 2000. ,
DOI : 10.1006/jfan.1999.3550
Universal Bounds for the Littlewood-Paley First-Order Moments of the 3D Navier-Stokes Equations, Communications in Mathematical Physics, vol.72, issue.7, pp.301-315, 2009. ,
DOI : 10.1002/mana.3210040121
Geophysical Fluid Dynamics, 1979. ,
Stationary Navier???Stokes equations with critically singular external forces: Existence and stability results, Advances in Mathematics, vol.241, pp.1371-161, 2013. ,
DOI : 10.1016/j.aim.2013.01.016
Méthodes d'analyse harmonique pour l'´ etude deséquationsdeséquations de Navier-Stokes, Thèse de doctorat de l'université de Marne-la-Vallée, 2007. ,
An Experimental Investigation of the Circumstances Which Determine Whether the Motion of Water Shall Be Direct or Sinuous, and of the Law of Resistance in Parallel Channels, Philosophical Transactions of the Royal Society of London, vol.174, issue.0, pp.935-982, 1883. ,
DOI : 10.1098/rstl.1883.0029
Weather prediction by Numerical Process, 1922. ,
DOI : 10.1017/CBO9780511618291
Chance et Chaos, 1991. ,
Liouville type theorem for stationnary Navier-Stokes equations, Nonlinearity, vol.29, p.21912195, 2015. ,
A Liouville type theorem for steady-state Navier-Stokes equations, Journ??es ??quations aux d??riv??es partielles, 2016. ,
DOI : 10.5802/jedp.650
URL : http://arxiv.org/pdf/1611.01563
On the Effect of the Internal Friction of Fluids on the Motion of Pendulums. Transactions of the Cambridge Philosophical Society, pp.8-106, 1851. ,
Navier-Stokes Equations. Theory and Numerical Analysis, Studies in Mathematics and its Applications, 1984. ,
A First Course in Turbulence, 1972. ,
An album of fluid motion, 1982. ,
Free turbulence on R 3 and T 3, Dynamics of PDE, vol.7, pp.107-160, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00733839
Turbulence model for CFD, 1994. ,
A note on Gevrey class regularity for the solutions of the Navier-Stokes equations, Journal of Mathematical Analysis and Applications, vol.167, issue.2, pp.588-595, 1992. ,
DOI : 10.1016/0022-247X(92)90226-4