H. Abidi, R??sultats de r??gularit?? de solutions axisym??triques pour le syst??me de Navier???Stokes, Bulletin des Sciences Math??matiques, vol.132, issue.7, pp.592-624, 2008.
DOI : 10.1016/j.bulsci.2007.10.001

J. Anker and L. Ji, Heat Kernel and Green Function Estimates on Noncompact Symmetric Spaces, Geometric And Functional Analysis, vol.9, issue.6, pp.1035-1091, 1999.
DOI : 10.1007/s000390050107

URL : https://hal.archives-ouvertes.fr/hal-00022962

J. Anker, V. Pierfelice, and M. Vallarino, Schr??dinger Equations on Damek???Ricci Spaces, Communications in Partial Differential Equations, vol.17, issue.6, pp.976-997, 2011.
DOI : 10.1007/s00209-007-0279-0

P. Auscher, T. Coulhon, X. T. Duong, and S. Hofmann, Riesz transform on manifolds and heat kernel regularity, Annales Scientifiques de l?????cole Normale Sup??rieure, vol.37, issue.6, pp.911-957, 2004.
DOI : 10.1016/j.ansens.2004.10.003

URL : https://hal.archives-ouvertes.fr/hal-00096334

P. Auscher and D. Frey, A new proof for Koch and Tataru's result on the well-posedness of Navier- Stokes equations, 2013.

D. Bakry and M. Ledoux, A logarithmic Sobolev form of the Li-Yau parabolic inequality, Revista Matem??tica Iberoamericana, vol.22, issue.2, pp.683-702, 2006.
DOI : 10.4171/RMI/470

URL : https://hal.archives-ouvertes.fr/hal-00353946

J. Bourgain and N. Pavlovi´cpavlovi´c, 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

L. Caffarelli, R. Kohn, and L. Nirenberg, 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

M. Cannone and Y. Meyer, Littlewood???Paley decomposition and Navier???Stokes equations, Methods and Applications of Analysis, vol.2, issue.3, pp.307-319, 1995.
DOI : 10.4310/MAA.1995.v2.n3.a4

G. Carron, Estimes des noyaux de Green et de la chaleur sur les espaces symtriques, Anal, pp.197-205, 2010.
DOI : 10.2140/apde.2010.3.197

URL : http://arxiv.org/abs/0802.3111

J. Chemin, I. Gallagher, and M. Paicu, Global regularity for some classes of large solutions to the Navier-Stokes equations, Annals of Mathematics, vol.173, issue.2, pp.983-1012, 2011.
DOI : 10.4007/annals.2011.173.2.9

URL : https://hal.archives-ouvertes.fr/hal-00294203

T. Coulhon, Heat kernel estimates, Sobolev-type inequalities and Riesz transform on noncompact Riemannian manifolds, Analysis and geometry of metric measure spaces, CRM Proc. Lecture Notes, pp.55-65, 2013.

M. Czubak and C. H. Chan, Non-uniqueness of the Leray-Hopf solutions in the hyperbolic setting, Dynamics of PDE, vol.10, issue.1, pp.43-77, 2013.

M. Czubak and C. H. Chan, Remarks on the weak formulation of the Navier-Stokes equations on the 2D hyperbolic space, preprint, 2013.

E. Damek and F. Ricci, A class of nonsymmetric harmonic Riemannian spaces, Bulletin of the American Mathematical Society, vol.27, issue.1, pp.139-142, 1992.
DOI : 10.1090/S0273-0979-1992-00293-8

O. Druet, Nonlinear analysis on manifolds, Lectures Notes

D. G. Ebin and J. E. Marsden, Groups of Diffeomorphisms and the Motion of an Incompressible Fluid, The Annals of Mathematics, vol.92, issue.1, pp.92-102, 1970.
DOI : 10.2307/1970699

P. Erbelein, Geometry of non positively curved manifolds, Chicago Lectures in Mathematics, vol.449, 1996.

H. Fujita and T. Kato, On the Navier-Stokes initial value problem. I, Archive for Rational Mechanics and Analysis, vol.128, issue.4, pp.269-315, 1961.
DOI : 10.1007/BF00276188

G. Furioli, P. G. Lemarié-rieusset, and E. Terraneo, Uniqueness in L 3 (R 3 ) and other functional limit spaces for Navier-Stokes equations, Rev. Mat. Iberoamericana, vol.16, issue.3, pp.605-667, 2000.

I. Gallagher and F. Planchon, On Global Infinite Energy Solutions??to the Navier-Stokes Equations??in Two Dimensions, Archive for Rational Mechanics and Analysis, vol.161, issue.4, pp.307-337, 2002.
DOI : 10.1007/s002050100175

S. Gallot, D. Hulin, and J. Lafontaine, Riemannian geometry, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00002870

Y. Giga and T. Miyakawa, Solutions in Lr of the Navier-Stokes initial value problem, Archive for Rational Mechanics and Analysis, vol.74, issue.3, pp.267-281, 1985.
DOI : 10.1007/BF00276875

A. Grigor´yangrigor´yan and M. Noguchi, The Heat Kernel on Hyperbolic Space, Bulletin of the London Mathematical Society, vol.30, issue.6, pp.643-650, 1998.
DOI : 10.1112/S0024609398004780

E. Hebey, Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities, Courant Lectures in Mathematics, vol.5, 2000.
DOI : 10.1090/cln/005

S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Math. Soc, vol.34, 1978.
DOI : 10.1090/gsm/034

E. Hopf, ??ber die Anfangswertaufgabe f??r die hydrodynamischen Grundgleichungen. Erhard Schmidt zu seinem 75. Geburtstag gewidmet, Mathematische Nachrichten, vol.4, issue.1-6, pp.213-231, 1951.
DOI : 10.1002/mana.3210040121

J. Jost, Riemannian geometry and geometric analysis, Universitext, 2008.
DOI : 10.1007/978-3-642-21298-7

T. Kato, Strong L p solutions of the Navier-Stokes equations in Rm with applications to weak solutions, Math. Zeit, vol.187, p.471480, 1984.

C. E. Kenig and G. Koch, 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, pp.159-187, 2011.
DOI : 10.1016/j.anihpc.2010.10.004

B. Khesin and G. Misiolek, Euler and NavierStokes equations on the hyperbolic plane, Proc. Nat. Acad. Sci, 2012.

H. Koch and D. Tataru, Well-posedness for the Navier???Stokes Equations, Advances in Mathematics, vol.157, issue.1, pp.22-35, 2001.
DOI : 10.1006/aima.2000.1937

K. Kodaira, Harmonic fields in Riemannian manifolds (generalized potential theory) , Ann, pp.587-665, 1949.

J. Leray, Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Mathematica, vol.63, issue.0, pp.193-248, 1993.
DOI : 10.1007/BF02547354

P. Li and S. Yau, On the parabolic kernel of the Schr??dinger operator, Acta Mathematica, vol.156, issue.0, pp.153-201, 1986.
DOI : 10.1007/BF02399203

F. Lin, A new proof of the Caffarelli-Kohn-Nirenberg theorem, Communications on Pure and Applied Mathematics, vol.51, issue.3, pp.241-257, 1998.
DOI : 10.1002/(SICI)1097-0312(199803)51:3<241::AID-CPA2>3.0.CO;2-A

P. Lions and N. Masmoudi, UNIQUENESS OF MILD SOLUTIONS OF THE NAVIER-STOKES SYSTEM IN LN, Communications in Partial Differential Equations, vol.26, issue.11-12, pp.11-12, 2001.
DOI : 10.1081/PDE-100107819

H. P. Mckean, An upper bound to the spectrum of $\Delta $ on a manifold of negative curvature, Journal of Differential Geometry, vol.4, issue.3, pp.359-366, 1970.
DOI : 10.4310/jdg/1214429509

M. Mitrea and M. Taylor, Navier-Stokes equations on Lipschitz domains in Riemannian manifolds, Mathematische Annalen, vol.321, issue.4, pp.955-987, 2001.
DOI : 10.1007/s002080100261

J. Nash, Continuity of Solutions of Parabolic and Elliptic Equations, American Journal of Mathematics, vol.80, issue.4, pp.931-954, 1958.
DOI : 10.2307/2372841

C. Oseen, Sur les formules de Green généralisées qui se présentent dans l'hydrodynamique et sur quelques unes de leurs applications premì ere partie, Acta Matematica, pp.205-284, 1911.
DOI : 10.1007/bf02393128

C. Oseen, Sur les formules de Green généralisées qui se présentent dans l'hydrodynamique et sur quelques unes de leurs applications (seconde partie, Acta Matematica, pp.97-192, 1912.
DOI : 10.1007/bf02393128

E. M. Ouhabaz, L p contraction semigroups for vector valued functions, Positivity, vol.3, issue.1, pp.83-93, 1999.
DOI : 10.1023/A:1009711107390

URL : https://hal.archives-ouvertes.fr/hal-00693892

E. Pedon, Harmonic analysis for differential forms on complex hyperbolic spaces, Journal of Geometry and Physics, vol.32, issue.2, pp.102-130, 1999.
DOI : 10.1016/S0393-0440(99)00026-1

URL : https://hal.archives-ouvertes.fr/hal-00160424

F. Planchon, Global strong solutions in Sobolev or Lebesgue spaces to the incompressible Navier-Stokes equations in ???3, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.13, issue.3, pp.13-319, 1996.
DOI : 10.1016/S0294-1449(16)30107-X

. Volker-priebe, Solvability of the Navier-Stokes equations on manifolds with boundary, Manuscripta Math, pp.145-159, 1994.

A. G. Setti, A lower bound for the spectrum of the Laplacian in terms of sectional and Ricci curvature, Proceedings of the american mathematical society, pp.277-282, 1991.
DOI : 10.1090/S0002-9939-1991-1043421-3

R. Strichartz, Analysis of the Laplacian on the complete Riemannian manifold, Journal of Functional Analysis, vol.52, issue.1, pp.48-79, 1983.
DOI : 10.1016/0022-1236(83)90090-3

T. Tao, A quantitative formulation of the global regularity problem for the periodic Navier-Stokes equation, Dyn. Partial Differ, Eq, vol.4, issue.4, pp.293-302, 2007.

M. Taylor, Partial Differential Equations III: Nonlinear Equations, Nonlinear equations, Applied Math-ematical Sciences, vol.117, 2011.

M. Uno, On Sectional Curvature of Boggino-Damek-Ricci Type Spaces, Tokyo Journal of Mathematics, vol.23, issue.2, pp.417-427, 2000.
DOI : 10.3836/tjm/1255958680

N. Th and . Varopoulos, The heat kernel on Lie groups, Rev. Mat. Iberoamericana, vol.12, issue.1, pp.147-186, 1996.

F. B. Weissler, The Navier-Stokes initial value problem in Lp, Archive for Rational Mechanics and Analysis, vol.29, issue.3, pp.219-230, 1980.
DOI : 10.1007/BF00280539

E. Zuazua, Large Time Asymptotics For Heat and Dissipative Wave Equations, Lectures Notes, 2003.