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Martel Yvan
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Biography and Current Works

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Main Publications and Links

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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