]. T. Aubin, ´ Equations différentielles non linéaires etprobì eme de Yamabe concernant la courbure scalaire, J. Math. Pures Appl, vol.55, issue.9, pp.269-296, 1976.
DOI : 10.1007/bfb0076620

H. Bahouri, J. Chemin, and R. Danchin, Fourier Analysis and Nonlinear Partial Differential Equations, volume 343 of Grundlehren der mathematischen Wissenschaften, 2011.

H. Bahouri and P. Gérard, 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

P. Bizo´nbizo´n, T. Chmaj, and Z. Tabor, Formation of singularities for equivariant (2+1)-dimensional wave maps into the 2-sphere, Nonlinearity, vol.14, issue.5, pp.1041-1053, 2001.
DOI : 10.1088/0951-7715/14/5/308

J. Bourgain and W. Wang, Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.25, issue.4, pp.197-215, 1997.

P. Brenner, On scattering and everywhere defined scattering operators for nonlinear Klein-Gordon equations, Journal of Differential Equations, vol.56, issue.3, pp.310-344, 1985.
DOI : 10.1016/0022-0396(85)90083-X

F. E. Browder, On non-linear wave equations, Mathematische Zeitschrift, vol.77, issue.1, pp.249-264, 1962.
DOI : 10.1007/BF01162382
URL : http://www.digizeitschriften.de/download/PPN266833020_0080/PPN266833020_0080___log34.pdf

A. Bulut, M. Czubak, D. Li, N. Pavlovi´cpavlovi´c, and X. Zhang, Stability and Unconditional Uniqueness of Solutions for Energy Critical Wave Equations in High Dimensions, Communications in Partial Differential Equations, vol.118, issue.4, pp.575-607, 2013.
DOI : 10.1215/S0012-7094-07-13825-0

T. Cazenave, Semilinear Schrödinger Equations, Courant Lecture Notes in Mathematics. AMS, vol.10, 2003.

T. Cazenave, J. Shatah, and A. Tahvildar-zadeh, Harmonic maps of the hyperbolic space and development of singularities in wave maps and Yang-Mills fields, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.68, issue.3, pp.315-349, 1998.

S. Chow and J. K. Hale, Methods of Bifurcation Theory, volume 251 of Grundlehren der mathematischen Wissenschaften, 1982.

F. M. Christ and M. I. Weinstein, Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation, Journal of Functional Analysis, vol.100, issue.1, pp.87-109, 1991.
DOI : 10.1016/0022-1236(91)90103-C

C. Collot, Type II blow up for the energy supercritical wave equation, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01288578

R. Côte, On the Soliton Resolution for Equivariant Wave Maps to the Sphere, Communications on Pure and Applied Mathematics, vol.127, issue.2, pp.1946-2004, 2015.
DOI : 10.1002/cpa.21545

R. Côte, C. Kenig, A. Lawrie, and W. Schlag, Profiles for the radial focusing 4d energycritical wave equation, 2014.

R. Côte, C. E. Kenig, A. Lawrie, and W. Schlag, Characterization of large energy solutions of the equivariant wave map problem: I, American Journal of Mathematics, vol.137, issue.1, pp.139-207, 2015.
DOI : 10.1353/ajm.2015.0002

R. Côte, C. E. Kenig, and F. Merle, Scattering Below Critical Energy for the Radial 4D Yang-Mills Equation and for the 2D Corotational Wave Map System, Communications in Mathematical Physics, vol.56, issue.7, pp.203-225, 2008.
DOI : 10.1007/s00220-008-0604-4

R. Côte, Y. Martel, and F. Merle, Construction of multi-soliton solutions for the L 2 supercritical gKdV and NLS equations, Rev. Mat. Iberoam, vol.27, issue.1, pp.273-302, 2011.

R. Donninger, M. Huang, J. Krieger, and W. Schlag, Exotic blowup solutions for the u 5 focusing wave equation in R 3 . Michigan Math, J, vol.63, issue.3, pp.451-501, 2014.

R. Donninger and J. Krieger, Nonscattering solutions and blowup at infinity for the critical wave equation, Mathematische Annalen, vol.3, issue.2, pp.89-163, 2013.
DOI : 10.1007/s00208-013-0898-1

R. Donninger and B. Schörkhuber, Stable blow up dynamics for energy supercritical wave equations, Transactions of the American Mathematical Society, vol.366, issue.4, pp.2167-2189, 2014.
DOI : 10.1090/S0002-9947-2013-06038-2
URL : http://arxiv.org/abs/1207.7046

R. Donninger and B. Schörkhuber, Stable blowup for wave equations in odd space dimensions, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 2015.
DOI : 10.1016/j.anihpc.2016.09.005

T. Duyckaerts, C. E. Kenig, and F. Merle, Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation, Journal of the European Mathematical Society, vol.13, issue.3, pp.533-599, 2011.
DOI : 10.4171/JEMS/261
URL : https://hal.archives-ouvertes.fr/hal-00460872

T. Duyckaerts, C. E. Kenig, and F. Merle, Profiles of bounded radial solutions of the focusing, energy-critical wave equation, Geometric and Functional Analysis, vol.110, issue.3, pp.639-698, 2012.
DOI : 10.1007/s00039-012-0174-7

T. Duyckaerts, C. E. Kenig, and F. Merle, Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case, Journal of the European Mathematical Society, vol.14, issue.5, pp.1389-1454, 2012.
DOI : 10.4171/JEMS/336
URL : https://hal.archives-ouvertes.fr/hal-00460872

T. Duyckaerts, C. E. Kenig, and F. Merle, Classification of the radial solutions of the focusing, energy-critical wave equation, Cambridge Journal of Mathematics, vol.1, issue.1, pp.75-144, 2013.
DOI : 10.4310/CJM.2013.v1.n1.a3

T. Duyckaerts and F. Merle, Dynamics of Threshold Solutions for Energy-Critical Wave Equation, International Mathematics Research Papers, 2008.
DOI : 10.1093/imrp/rpn002

W. Eckhaus and P. C. Schuur, The emergence of solitons of the korteweg-de vries equation from arbitrary initial conditions, Mathematical Methods in the Applied Sciences, vol.59, issue.1, pp.97-116, 1983.
DOI : 10.1002/mma.1670050108

L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics . AMS, vol.19, 1998.

K. O. Friedrichs, Symmetric hyperbolic linear differential equations, Communications on Pure and Applied Mathematics, vol.88, issue.2, pp.345-392, 1954.
DOI : 10.1002/cpa.3160070206
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.697.7231

Y. Giga and R. V. Kohn, Nondegeneracy of blowup for semilinear heat equations, Communications on Pure and Applied Mathematics, vol.55, issue.6, pp.845-884, 1989.
DOI : 10.1002/cpa.3160420607

J. Ginibre, A. Soffer, and G. Velo, The global Cauchy problem for the critical non-linear wave equation, Journal of Functional Analysis, vol.110, issue.1, pp.96-130, 1992.
DOI : 10.1016/0022-1236(92)90044-J

J. Ginibre and G. Velo, Generalized Strichartz Inequalities for the Wave Equation, Journal of Functional Analysis, vol.133, issue.1, pp.50-68, 1995.
DOI : 10.1006/jfan.1995.1119

M. Grillakis, Regularity and Asymptotic Behavior of the Wave Equation with a Critical Nonlinearity, The Annals of Mathematics, vol.132, issue.3, pp.485-509, 1990.
DOI : 10.2307/1971427

S. Gustafson, K. Kang, and T. Tsai, Schr??dinger flow near harmonic maps, Communications on Pure and Applied Mathematics, vol.34, issue.4, pp.463-499, 2007.
DOI : 10.1002/cpa.20143
URL : http://arxiv.org/abs/math/0504497

M. Hillairet and P. , Smooth type II blow-up solutions to the four-dimensional energy-critical wave equation, Analysis & PDE, vol.5, issue.4, pp.777-829, 2012.
DOI : 10.2140/apde.2012.5.777
URL : https://hal.archives-ouvertes.fr/hal-00934753

R. Van-der-hout, On the nonexistence of finite time bubble trees in symmetric harmonic map heat flows from the disk to the 2-sphere, Journal of Differential Equations, vol.192, issue.1, pp.188-201, 2003.
DOI : 10.1016/S0022-0396(03)00043-3

S. Ibrahim, N. Masmoudi, and K. Nakanishi, Scattering threshold for the focusing nonlinear Klein???Gordon equation, Analysis & PDE, vol.4, issue.3, pp.405-460, 2011.
DOI : 10.2140/apde.2011.4.405

J. Jendrej, Bounds on the Speed of Type II Blow-up for the Energy Critical Wave Equation in the Radial Case, International Mathematics Research Notices, vol.2016, issue.21, 2015.
DOI : 10.1093/imrn/rnv365

J. Jendrej, Construction of type II blow-up solutions for the energy-critical wave equation in dimension 5, Journal of Functional Analysis, vol.272, issue.3, 2015.
DOI : 10.1016/j.jfa.2016.10.019

J. Jendrej, Nonexistence of radial two-bubbles with opposite signs for the energy-critical wave equation, 2015.

H. Jia and C. E. Kenig, Asymptotic decomposition for semilinear wave and equivariant wave map equations, 2015.

K. Jörgens, Das Anfangswertproblem in Gro???en f???r eine Klasse nichtlinearer Wellengleichungen, Mathematische Zeitschrift, vol.4, issue.1, pp.295-308, 1961.
DOI : 10.1007/BF01180181

L. V. Kapitanski, Global and Unique Weak Solutions of Nonlinear Wave Equations, Mathematical Research Letters, vol.1, issue.2, pp.211-223, 1994.
DOI : 10.4310/MRL.1994.v1.n2.a9

J. B. Keller, On solutions of nonlinear wave equations, Communications on Pure and Applied Mathematics, vol.234, issue.4, pp.523-530, 1957.
DOI : 10.1002/cpa.3160100404

C. E. Kenig and F. Merle, 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

C. E. Kenig and F. Merle, 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

C. E. Kenig and F. Merle, Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications, American Journal of Mathematics, vol.133, issue.4, pp.1029-1065, 2011.
DOI : 10.1353/ajm.2011.0029
URL : http://arxiv.org/abs/0810.4834

J. Krieger, K. Nakanishi, and W. Schlag, Center-stable manifold of the ground state in the energy space for the critical wave equation, Mathematische Annalen, vol.127, issue.3???4, pp.1-50, 2015.
DOI : 10.1007/s00208-014-1059-x

J. Krieger and W. Schlag, Full range of blow up exponents for the quintic wave equation in three dimensions, Journal de Math??matiques Pures et Appliqu??es, vol.101, issue.6, pp.873-900, 2014.
DOI : 10.1016/j.matpur.2013.10.008

J. Krieger and W. Schlag, Large global solutions for energy supercritical nonlinear wave equations on R 3+1, J. Anal. Math

J. Krieger, W. Schlag, and D. Tataru, Renormalization and blow up for charge one equivariant critical wave maps, Inventiones mathematicae, vol.127, issue.2, pp.543-615, 2008.
DOI : 10.1007/s00222-007-0089-3
URL : http://arxiv.org/abs/math/0610248

J. Krieger, W. Schlag, and D. Tataru, Slow blow-up solutions for the $H^1({\mathbb R}^3)$ critical focusing semilinear wave equation, Duke Mathematical Journal, vol.147, issue.1, pp.1-53, 2009.
DOI : 10.1215/00127094-2009-005

A. Lawrie and S. Oh, A Refined Threshold Theorem for (1??+??2)-Dimensional Wave Maps into Surfaces, Communications in Mathematical Physics, vol.224, issue.2, pp.989-999, 2016.
DOI : 10.1007/s00220-015-2513-7

Y. Y. Li, Prescribing Scalar Curvature on Sn and Related Problems, Part I, Journal of Differential Equations, vol.120, issue.2, pp.319-410, 1995.
DOI : 10.1006/jdeq.1995.1115
URL : http://doi.org/10.1006/jdeq.1995.1115

Y. Martel, Asymptotic N -soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations, American Journal of Mathematics, vol.127, issue.5, pp.1103-1140, 2005.
DOI : 10.1353/ajm.2005.0033

Y. Martel and F. Merle, Instability of solitons for the critical generalized Korteweg???de Vries equation, Geometric and Functional Analysis, vol.11, issue.1, pp.74-123, 2001.
DOI : 10.1007/PL00001673
URL : https://hal.archives-ouvertes.fr/hal-00189836

Y. Martel and F. Merle, Construction of Multi-Solitons for the Energy-Critical Wave Equation in Dimension 5, Archive for Rational Mechanics and Analysis, vol.34, issue.11, 2015.
DOI : 10.1007/s00205-016-1018-7

Y. Martel, F. Merle, and P. , Blow up and near soliton dynamics for the L^2 critical gKdV equation, S??minaire Laurent Schwartz ??? EDP et applications, vol.212, issue.1, pp.59-140, 2014.
DOI : 10.5802/slsedp.28

Y. Martel, F. Merle, and P. , Blow up for the critical gKdV equation III: exotic regimes, Ann. Sc. Norm. Super. Pisa Cl. Sci, vol.XIV, pp.575-631, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00843250

Y. Martel, F. Merle, P. Raphaël, and J. Szeftel, Near soliton dynamics and singularity formation for $ L^2$ critical problems, Russian Mathematical Surveys, vol.69, issue.2, pp.261-290, 2014.
DOI : 10.1070/RM2014v069n02ABEH004888
URL : http://arxiv.org/abs/1412.2375

Y. Martel and P. , Strongly interacting blow up bubbles for the mass critical NLS, 2015.

H. Matano and F. Merle, Classification of type I and type II behaviors for a supercritical nonlinear heat equation, Journal of Functional Analysis, vol.256, issue.4, pp.992-1064, 2009.
DOI : 10.1016/j.jfa.2008.05.021

F. Merle, Construction of solutions with exactly k blow-up points for the Schr??dinger equation with critical nonlinearity, Communications in Mathematical Physics, vol.14, issue.2, pp.223-240, 1990.
DOI : 10.1007/BF02096981

F. Merle and P. , Profiles and Quantization of the Blow Up Mass for Critical Nonlinear Schr???dinger Equation, Communications in Mathematical Physics, vol.87, issue.3, pp.675-704, 2005.
DOI : 10.1007/s00220-004-1198-0

F. Merle, P. Raphaël, and I. Rodnianski, Blowup dynamics for smooth data equivariant solutions to the critical Schr??dinger map problem, Inventiones mathematicae, vol.56, issue.7, pp.249-365, 2013.
DOI : 10.1007/s00222-012-0427-y

F. Merle and H. Zaag, Determination of the blow-up rate for the semilinear wave equation, American Journal of Mathematics, vol.125, issue.5, pp.1147-1164, 2003.
DOI : 10.1353/ajm.2003.0033
URL : https://hal.archives-ouvertes.fr/hal-00096477

F. Merle and H. Zaag, Determination of the blow-up rate for a critical semilinear wave equation, Mathematische Annalen, vol.125, issue.2, pp.395-416, 2005.
DOI : 10.1007/s00208-004-0587-1

N. Mizoguchi, Rate of Type II blowup for a semilinear heat equation, Mathematische Annalen, vol.338, issue.4, pp.839-877, 2007.
DOI : 10.1007/s00208-007-0133-z

C. S. Morawetz and W. A. Strauss, Decay and scattering of solutions of a nonlinear relativistic wave equation, Communications on Pure and Applied Mathematics, vol.114, issue.1, pp.1-31, 1972.
DOI : 10.1002/cpa.3160250103

K. Nakanishi and W. Schlag, Global dynamics above the ground state energy for the focusing nonlinear Klein???Gordon equation, Journal of Differential Equations, vol.250, issue.5, pp.2299-2333, 2011.
DOI : 10.1016/j.jde.2010.10.027

K. Nakanishi and W. Schlag, Global Dynamics Above the Ground State for the Nonlinear Klein???Gordon Equation Without a Radial Assumption, Archive for Rational Mechanics and Analysis, vol.16, issue.3, pp.809-851, 2011.
DOI : 10.1007/s00205-011-0462-7

M. Del-pino, M. Musso, F. Pacard, and A. Pistoia, Large energy entire solutions for the Yamabe equation, Journal of Differential Equations, vol.251, issue.9, pp.2568-2597, 2011.
DOI : 10.1016/j.jde.2011.03.008
URL : https://hal.archives-ouvertes.fr/hal-00851580

C. Ortoleva and G. Perelman, Nondispersive vanishing and blow up at infinity for the energy critical nonlinear Schrödinger equation in R 3 . Algebra i Analiz, pp.162-192, 2013.

L. E. Payne and D. H. Sattinger, Saddle points and instability of nonlinear hyperbolic equations, Israel Journal of Mathematics, vol.47, issue.3-4, pp.273-303, 1975.
DOI : 10.3792/pja/1195526303

G. Perelman, Blow Up Dynamics for Equivariant Critical Schr??dinger Maps, Communications in Mathematical Physics, vol.60, issue.4, pp.69-105, 2014.
DOI : 10.1007/s00220-014-1916-1

A. Pistoia and T. Weth, Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.24, issue.2, pp.325-340, 2007.
DOI : 10.1016/j.anihpc.2006.03.002

P. Raphaël and J. Szeftel, Existence and uniqueness of minimal blow-up solutions to an inhomogeneous mass critical NLS, Journal of the American Mathematical Society, vol.24, issue.2, pp.471-546, 2011.
DOI : 10.1090/S0894-0347-2010-00688-1

I. Rodnianski and P. , Stable blow up dynamics for critical corotational wave maps and the equivariant Yang Mills problem, Publ. Math. Inst. HautesÉtudesHautes´HautesÉtudes Sci, vol.115, pp.1-122, 2012.

I. Rodnianski and J. Sterbenz, -model, Annals of Mathematics, vol.172, issue.1, pp.187-242, 2010.
DOI : 10.4007/annals.2010.172.187
URL : https://hal.archives-ouvertes.fr/hal-00631136

C. Rodriguez, Profiles for the radial focusing energy-critical wave equation in odd dimensions, 2014.

R. Schweyer, Type II blow-up for the four dimensional energy critical semi linear heat equation, Journal of Functional Analysis, vol.263, issue.12, pp.3922-3983, 2012.
DOI : 10.1016/j.jfa.2012.09.015
URL : https://hal.archives-ouvertes.fr/hal-00942940

I. E. Segal, Non-Linear Semi-Groups, The Annals of Mathematics, vol.78, issue.2, pp.339-364, 1963.
DOI : 10.2307/1970347

J. Shatah and M. Struwe, Well-posedness in the energy space for semilinear wave equations with critical growth, Internat. Math. Res. Notices, vol.7, pp.303-309, 1994.

J. Shatah and M. Struwe, Geometric Wave Equations, Courant Lecture Notes in Mathematics. AMS, vol.2, 2000.
DOI : 10.1090/cln/002

J. Shatah and A. Tahvildar-zadeh, On the cauchy problem for equivariant wave maps, Communications on Pure and Applied Mathematics, vol.64, issue.5, pp.719-754, 1994.
DOI : 10.1002/cpa.3160470507

W. A. Strauss, Existence of solitary waves in higher dimensions, Communications in Mathematical Physics, vol.62, issue.2, pp.149-162, 1977.
DOI : 10.1007/BF01626517

M. Struwe, Globally regular solutions to the u 5 klein-gordon equation, Ann. Scuola Norm. Pisa Cl. Sci, vol.15, pp.495-513, 1988.

M. Struwe, Equivariant wave maps in two space dimensions, Communications on Pure and Applied Mathematics, vol.45, issue.7, pp.815-823, 2003.
DOI : 10.1002/cpa.10074

G. Talenti, Best constant in Sobolev inequality, Annali di Matematica Pura ed Applicata, Series 4, vol.110, issue.1, pp.353-372, 1976.
DOI : 10.1007/BF02418013
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.615.4193

T. Tao, Nonlinear Dispersive Equations: Local and Global Analysis, CBMS Reg. Conf. Series in Math. AMS, 2006.
DOI : 10.1090/cbms/106

P. Topping, An example of a nontrivial bubble tree in the harmonic map heat flow, Harmonic Morphisms, Harmonic Maps and Related Topics. Chapman and Hall/CRC, 1999.

P. Topping, Repulsion and quantization in almost-harmonic maps, and asymptotics of the harmonic map flow, Annals of Mathematics, vol.159, issue.2, pp.465-534, 2004.
DOI : 10.4007/annals.2004.159.465