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Martel Yvan
PROFESSEUR

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Bureau : 6:10-18&A
Téléphone : +33169334947
Département/Laboratoire/Service : CA/DER/DEP/MATH
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Bibliographie & travail en cours

Biographie: 

EDUCATION

2000, Habilitation à Diriger des Recherches, Université de Cergy-Pontoise

1993-1996, Ph.D. Université Pierre et Marie Curie. Supervisor: T. Cazenave

1992-1993, DEA Analyse nonlinéaire et analyse numérique

1989-1992, Ecole Polytechnique

POSITIONS

Current: Professor at École polytechnique since September 2012.

Professor at université de Versailles-Saint-Quentin-en-Yvelines since September 2004, on leave at Ecole polytechnique since September 2012

Junior Member of Institut Universitaire de France 2008-2012

Part-time Associated Professor at Ecole polytechnique from September 2004 to August 2012

Full-time Associated Professor at Ecole polytechnique from September 2002 to August 2004

Assistance Professor at université de Cergy-Pontoise from September 1997 to August 2004, on leave at Ecole Polytechnique from September 2002 to August 2004

INSTITUTIONAL RESPONSABILITIES

2012-2017, Head of CMLS (centre de mathématiques Laurent Schwartz) from 2012 to January 2017.

2012-2015, Member of the national CNRS Committee in Mathematics (committee in charge of hiring and promoting CNRS permanent junior and senior researchers).

2008-2011, Head of laboratoire de mathématiques de Versailles from June 2008 to January 2012.

INVITED PRESENTATIONS

2018, Invited Speaker at the International Congress of Mathematicians (Rio de Janeiro)

2015, Member of Mathematical Science Research Institute (Berkeley).

2011, Fabes-Riviere Lecture (Mineapolis)

2008, Invited Speaker at the European Congress of Mathematics (Amsterdam, 45 min)

ORGANISATION OF INTERNATIONAL CONFERENCES

2016, Organisation IHES semester Nonlinear Waves (with ERC BLOWDISOL) including to two conferences and a PDE summer school organised at IHES https://www.ihes.fr/en/trimester-on-nonlinear-waves/

Fall 2015, MSRI Program, Berkeley 

2011, International conference in nonlinear PDE, Santiago, Chile.

Publications et Liens

Publications: 

Updated January 2020

ARTICLES - preliminary versions on arxiv: https://arxiv.org/search/math?searchtype=author&query=Martel%2C+Y

[64] Yakine Bahri, Yvan Martel, Pierre Raphaël, Self-similar blow-up profiles for slightly supercritical nonlinear Schrödinger equations. Link arXiv: https://arxiv.org/pdf/1911.11457.pdf

[63] Raphaël Côte, Yvan Martel, Xu Yuan, Lifeng Zhao, Description and classification of 2-solitary waves for nonlinear damped Klein-Gordon equations. Link arXiv: https://arxiv.org/pdf/1908.09527.pdf

[62] Yvan Martel, Didier Pilod, Full family of flattening solitary waves for the mass critical generalized KdV equation. Link arXiv: https://arxiv.org/pdf/1903.10756.pdf

[61] Thierry Cazenave, Zheng Han, Yvan Martel, Blowup on an arbitrary compact set for a Schrödinger equation with nonlinear source term. Link arXiv: https://arxiv.org/pdf/1906.02983.pdf

[60] Michal Kowalczyk, Yvan Martel, Claudio Muñoz, Soliton dynamics for the 1D NLKG equation with symmetry and in the absence of internal modes. To appear in JEMS.

[59] Jacek Jendrej, Yvan Martel, Construction of multi-bubble solutions for the energy-critical wave equation in dimension 5. To appear in JMPA.

[58] Yvan Martel, Tien Vinh Nguyen, Construction of 2-solitons with logarithmic distance for the one-dimensional cubic Schrodinger system. DCDS A, 2020. DOI: https://doi.org/10.3934/dcds.2020087

[57] Thierry Cazenave, Yvan Martel, Lifeng Zhao, Solutions blowing up on any given compact set for the energy subcritical wave equation. JDE, 2020. DOI: https://doi.org/10.1016/j.jde.2019.08.030

[56] Thierry Cazenave, Yvan Martel, Lifeng Zhao, Solutions with prescribed local blow-up surface for the nonlinear wave equation. Adv. Nonlinear Stud., 2019. DOI: https://doi.org/10.1515/ans-2019-2059

[55] Thierry Cazenave, Yvan Martel, Lifeng Zhao, Finite-time blowup for a Schrödinger equation with nonlinear source term. DCDS A, 2019. DOI: https://doi.org/10.3934/dcds.2019050

[54] Y. Martel, F. Merle, Inelasticity of soliton collisions for the 5D energy critical wave equation. Inventiones Mathematicae, 2018. DOI: https://doi.org/10.1007/s00222-018-0822-0

[53] V. Combet, Y. Martel, Construction of multi-bubble solutions for the critical gKdV equation. SIAM J. Math. Anal., 50(4) (2018), 3715–3790. DOI: https://doi.org/10.1137/17M1140595

[52] R. Côte, Y. Martel, Multi-travelling waves for the nonlinear Klein-Gordon equation. Trans. Amer. Math. Soc. 370 (2018), 7461-7487. DOI: https://doi.org/10.1090/tran/7303

[51] Y. Martel, P. Raphaël, Strongly interacting blow up bubbles for the mass critical NLS. Annales scientifiques de l’École normale supérieure, 51, fascicule 3 (2018), 701-737. http://smf4.emath.fr/en/Publications/AnnalesENS/4_51/html/ens_ann-sc_51_701-737.php

[50] Y. Martel, D. Pilod, Construction of a minimal mass blow up solution of the modified Benjamin-Ono equation. Mathematische Annalen Volume 369, Issue 1-2, pp 153-245. DOI: https://doi.org/10.1007/s00208-016-1497-8

[49] M. Kowalczyk, Y. Martel, C. Muñoz, Nonexistence of small, odd breathers for a class of nonlinear wave equations. Lett Math Phys (2017) 107: 921. DOI: https://doi.org/10.1007/s11005-016-0930-y

[48] M. Kowalczyk, Y. Martel, C. Muñoz, Kink dynamics in the phi4 model: asymptotic stability for odd perturbations in the energy space. J. Amer. Math. Soc. 30 (2017), 769-798. DOI: https://doi.org/10.1090/jams/870

[47] V. Combet, Y. Martel, Sharp asymptotics for the minimal mass blow up solution of critical gKdV equation. Bulletin des Sciences Mathématiques Volume 141, Issue 2, March 2017, Pages 20–103. DOI: http://dx.doi.org/10.1016/j.bulsci.2017.01.001

[46] Y. Martel, F. Merle, Construction of multi-solitons for the energy-critical wave equation in dimension 5. Arch. Ration. Mech. Anal. 222 (2016), no. 3, 1113-1160. DOI: https://doi.org/10.1007/s00205-016-1018-7

[45] S. Le Coz, Y. Martel, P. Raphael, Minimal mass blow up solutions for a double power nonlinear Schrödinger equation. Revista Math. Iberoamericana, Volume 32, Issue 3, 2016, pp. 795–833. DOI: https://doi.org/10.4171/RMI/899

[44] Y. Martel, F. Merle, K. Nakanishi, P. Raphael, Codimension one threshold manifold for the critical gKdV equation. Comm. Math. Phys. 342 (2016), no. 3, 1075-1106. DOI: https://doi.org/10.1007/s00220-015-2509-3

[43] Y. Martel, F. Merle, On the nonexistence of pure multi-solitons for the quartic gKdV equation. Int Math Res Notices (2015) (3): 688-739.

[42] Y. Martel, F. Merle, P. Raphaël, Blow up for the critical gKdV equation III: exotic regimes. Annali della Scuola Normale Superiore de Pisa XIV, 575-631 (2015).

[41] Y. Martel, F. Merle, P. Raphaël, Blow up for the critical gKdV equation II: minimal mass dynamics. J. of Math. Eur. Soc. 17, 1855-1925 (2015).

[40] Y. Martel, F. Merle, P. Raphaël, Blow up for the critical gKdV equation I: dynamics near the soliton. Acta Math. 212 (2014), no. 1, 59–140.

[39] C. E. Kenig, Y. Martel, L. Robbiano, Local well-posedness and blow up in the energy space for a class of L2 critical dispersion generalized Benjamin-Ono equations, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 28, No. 6, 853-887 (2011).

[38] Y. Martel, F. Merle, Inelastic interaction of nearly equal solitons for the quartic gKdV equation, Invent. Math. 183, No. 3, 563-648 (2011).

[37] Y. Martel, F. Merle, Description of two soliton collision for the quartic gKdV equation, Ann. Math. (2) 174, No. 2, 757-857 (2011).

[36] R. Côte, Y. Martel, F. Merle, Construction of multi-soliton solutions for the L2-supercritical gKdV and NLS equations, Rev. Mat. Iberoam. 27, No. 1, 273-302 (2011).

[35] Y. Martel, F. Merle, Inelastic interaction of nearly equal solitons for the BBM equation, Discrete Contin. Dyn. Syst. 27, No. 2, 487-532 (2010).

[34] Y. Martel, F. Merle, T. Mizumachi, Description of the inelastic collision of two solitary waves for the BBM equation, Arch. Ration. Mech. Anal. 196, No. 2, 517-574 (2010).

[33] J. Krieger, Y. Martel, P. Raphaël, Two-soliton solutions to the three-dimensional gravitational Hartree equation, Communications on Pure and Applied Mathematics, 62 (2009) 1501-1550.

[32] Y. Martel, F. Merle, Stability of two soliton collision for nonintegrable gKdV equations, Communications in Mathematical Physics 286 (2009), 39-79.

[31] C.E. Kenig, Y. Martel, Asymptotic stability of solitons for the Benjamin-Ono equation, Revista Matematica Iberoamericana 25 (2009), 909-970.

[30] Y. Martel, F. Merle, Note on coupled linear systems related to two soliton collision for the quartic gKdV equation, Rev. Mat. Complut. 21 (2008), 327-349.

[29] Y. Martel, F. Merle, Asymptotic stability of solitons of the gKdV equations with a general nonlinearity, Math. Ann. 341 (2008), 391-427.

[28] Y. Martel, F. Merle, Refined asymptotics around solitons for the gKdV equations with a general nonlinearity, Discrete Contin. Dyn. Syst. 20 (2008), no. 2, 177-218.

[27] Y. Martel, Linear problems related to asymptotic stability of solitons of the generalized KdV equations, SIMA 38 (2006), 759-781.

[26] Y. Martel, F. Merle, Multi-solitary waves for nonlinear Schrodinger equations, Annales de l'IHP (C) Non Linear Analysis, 23 (2006), 849-864.

[25] Y. Martel, F. Merle, Tai-Peng Tsai, Stability in H1 of the sum of K solitary waves for some nonlinear Schrodinger equations, Duke Math. J. 133 (2006), 405-466.

[24] C. E. Kenig, Y. Martel, Global wellposedness in the energy space for a modified KP II equation via the Miura transform, Trans. Amer. Math. Soc. 358 (2006), 2447-2488.

[23] Y. Martel, Asymptotic N-soliton-like solutions of subcritical and critical generalized KdV equations, Amer. J. of Math. 127 (2005), 1103-1140.

[22] Y. Martel, F. Merle, Asymptotic stability of solitons for the gKdV equations revisited, Nonlinearity 18 (2005), 55-80.

[21] K. El Dika, Y. Martel, Stability of N solitary waves for the gBBM equations, Dyn. Partial Differ. Equ. 1 (2004), 401-437.

[20] A. de Bouard, Y. Martel, Nonexistence of L2 compact solutions of the Kadomtsev-Petviashvili II equation, Math. Annalen. 328 (2004), 525-544.

[19] C. Laurent, Y. Martel, Smoothness and exponential decay of L2-compact solutions of the generalized KdV equations, Comm. Partial Differential Equations 28 (2003), 2093-2107.

[18] Y. Martel, F. Merle, Tai-Peng Tsai, Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations, Comm. Math. Phys. 231 (2002), 347-373.

[17] Y. Martel, F. Merle, Nonexistence of blow up solution with minimal L2 mass for the critical gKdV equation, Duke Math. J. 115 (2002), 385-408.

[16] Y. Martel, F. Merle, Blow up in finite time and dynamics of blow up solutions for the critical generalized KdV equation, J. Amer. Math. Soc. 15 (2002), 617-664.

[15] Y. Martel, F. Merle, Stability of blowup profile and lower bounds on blowup rate for the critical generalized KdV equation, Ann. of Math. 155 (2002), 235-280.

[14] Y. Martel, F. Merle, Asymptotic stability of solitons for the subcritical generalized KdV equations, Arch. Ration. Mech. Anal. 157 (2001), 219-254. CORRECTION: Arch. Ration. Mech. Anal. 162 (2002), 191.

[13] Y. Martel, F. Merle, Instability of solitons for the critical generalized Korteweg-de Vries equation, Geom. Funct. Anal. 11 (2001) 74-123.

[12] Y. Martel, F. Merle, A Liouville theorem for the critical generalized Korteweg-de Vries equation, J. Math. Pures Appl. 79 (2000), 339-425.

[11] Y. Martel, Blow up for a class of quasilinear wave equations in one space dimension, Math. Meth. Appl. Sci. 23 (2000), 751-767.

[10] Y. Martel, Ph. Souplet, Small time boundary behavior of solutions of parabolic equations with noncompatible data, J. Math. Pures Appl. 79 (2000), 603-632.

[9] X. Cabré, Y. Martel, Existence versus explosion instantanée pour des équations de la chaleur linéaires avec potentiel singulier, C. R. Acad. Sci. 329, série I (1999), 973-978.

[8] Y. Martel, Dynamical instability of weak extremal solutions of nonlinear elliptic problems, Adv. Math. Sci. Appl. 9 (1999), 163-181.

[7] X. Cabré, Y. Martel, Weak eigenfunctions for the linearization of extremal elliptic problems, J. Funct. Anal. 156 (1998), 30-56.

[6] Y. Martel, Complete blow up and global behaviour of solutions of  $u_t-\Delta u= g(u)$, Ann. Inst. H. Poincaré, Anal. non lin. 15 (1998), 687-723.

[5] Y. Martel, Uniqueness of weak extremal solutions of nonlinear elliptic problems, Houston J. Math. 23 (1997), 161-168.

[4] Y. Martel, Blow up for the nonlinear Schrödinger equation in nonisotropic spaces, Nonlin. Anal., TMA 28 (1997), 1903-1908.

[3] H. Brezis, T. Cazenave, Y. Martel, A. Ramiandrisoa, Blow up for $u_t-\Delta u= g(u)$ revisited, Adv. Diff. Eq. 1 (1996), 73-91.

[2] Y. Martel, A nonlinear Airy equation, Comput. Appl. Math. 15 (1996), 1-17.

[1] Y. Martel, A wave equation with a Dirac distribution, Portugaliae Math. 52 (1995), 343-355.

 

 

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