Pierre RAPHAEL

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  • [44] Gerard, P.; Lenzman, E.; Pocovnicu, O.; Raphael, P., Two soliton dynamics with transient turbulent regime for the cubic half wave on the line, preprint 2016.

  • [43] Collot, C.; Raphael, P.; Szeftel, J. On the stability of self similar blow up for the energy super critical heat equation, to appear in Memoirs of the AMS.pdf

  • [42] Martel, Y.; Merle, F.;  Nakanishi, K., Raphael, P.; Codimension one threshold for the critical gKdV equation, Comm Math Phys 342 (2016), no3, 1075-1106.

  • [41] Hadzic, M.; Raphael, P. Melting and freezing for the Stefan problem, arxiv 2015.pdf

  • [40] Martel,Y.; Raphael, P., Strongly interacting blow up bubbles for the mass critical NLS, arxiv 2015.pdf

  • [39] Collot, C.; Merle, F.; Raphael, P., The flow near the ground state for the energy critical heat equation in large dimensions, to appear in Comm. Math. Phys.pdf

  • [38] Merle, F.;  Raphael, P.; Rodnianski, I, , Type II blow up for the energy critical supercritical NLS, Cambridge Math Jour. 3, n04, 439-617. pdf

  • [37] Raphael, P.; Schweyer. R., Quantized slow blow up dynamics for the corotational energy critical harmonic heat flow, Anal PDE 7 (2014), no 8, 1713-1805 pdf

  • [36] Merle, F.;  Raphael, P.; Szeftel, J, On collapsing ring blow up solutions to the super critical NLS, Duke Math Jour. 163 (2014), no 2, 369-431 pdf

  • [35] Raphael, P.; Schweyer, R., On the stability of chemotactic agregation, Math Annal 359 (2014), no 1-2, 267-377 pdf

  • [34] Krieger, J.; Lenzmann, E.; Raphael, P., Non dispersive solutions to the $L^2$ critical half wave equation, ARMA, 209 (2013), no 1, 61-129 pdf

  • [33] Martel, Y.; Merle, F.; Raphael, P.; Blow up for the critical gKdV equation III: exotic regimes, Ann Sc. Norm Super. Pisa. Cl. Sci (5) 14 (2015). no2, 575--631 pdf

  • [32] Martel, Y.; Merle, F.; Raphael, P.; Blow up for the critical gKdV equation II: minimal mass blow up, J. Eur. Math. Soc 17 (2015), no 8, 575--631. pdf

  • [31] Martel, Y.; Merle, F.; Raphael, P.; Blow up for the critical gKdV equation I: dynamics near the solitary wave, Acat Math 212 (2014), no 1, 59-140 pdf

  • [30]  Rapha\"el, P., Concentration compacité à la Kenig-Merle, séminaire Bourbaki, vol 2011/2012 Exposes 1043--1058, Asterisque no 352 (2013). (2011) pdf

  • [29] Raphael, Schweyer, Stable blow up dynamics for the corotational energy critical harmonic heat flow, Comm. Pure App. Math 66 (2013), no 3, 414-480 pdf

  • [28] Merle, Raphael, Rodnianski, Blow up dynamics of smooth equivariant solutions to the energy critical Schrodinger map, Invent Math 193 (2013), no 2, 249-365pdf

  • [27] Lecoz, S; Martel, Y.; Raphael, P., Minimal blow up solutions for a double power nonlinear Schrodinger equation, Rev. Mat. Iberoam. 32 (2016), no 3, 795--833.

  • [26] Merle, Raphael, Szeftel, The instability of Bourgain Wang solutions for the L^2 critical NLS, Amer. Math. Jour. 135 (2013) n0 4, 967-1017 pdf

  • [25] Hillairet, Raphael, Smooth type II blow up solutions to the energy critical focusing wave equations, Analysis and PDE's (5) 2012, no 4, 777-829 pdf

  • [24] Raphael, Rodnianski, Stable blow up dynamics for critical corotational wave maps and the equivariant Yang Mills problem, Publ. Math. Inst. Hautes Études Sci. 115 (2012), 1–122 pdf

  • [23] Lemou, Mehats, Raphael, Orbital stability of spherical systems,  Invent Math 187 (2012), no. 1, 145–194., pdf

  • [22] Raphael, Szeftel, Existence and uniqueness of minimal mass blow up solutions to an inhomogeneous L^2 critical NLS, J. Amer. Math. Soc 24 (2011) no2, 471-546, pdf

  • [21] Lemou, Mehats, Raphael, A new variational approach to the stability of gravitational systems, Comm Math Phys 302 (2011), no 1, 161-224 pdf

  • [20] Merle, F; Raphael, P., Szeftel, Stable self similar blow up for slightly L^2 super criticcal NLS, Geom Funct Anal 20 (2010) no 4, 1028-1071, pdf

  • [19] Krieger, J.; Martel, Y.; Raphael, P., Two solitons solutions to the three dimensional gravitational Hartree equation, Comm. Pure App. Math 62 (2009), no 11, 1501-1550.pdf
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  • [18] Raphael, P.; Szeftel, J., Standing ring blow up solutions to the N dimensional quintic NLS, Comm. Math. Phys. 290 (2009), no 3, 973-996 pdf

  • [17] Krieger, J.; Lenzmann, E.; Raphael, P., On stability of pseudo-conformal blow up for L^2 critical NLS Hartree, Annales Henri Poincare 10 (2009), no 6, 1159-1205.pdf

  • [16] Lemou, M.; Mehats, F.; Raphael, P., Stable ground states for the relativistic gravitational Vlasov-Poisson system, Comm PDE 34 (2009), no 7-9, 703-721.

  • [15] Lemou, M.; Mehats, F.; Raphael, P., Stable self similar blow up solutions to the relativistic gravitational Vlasov-Poisson system,  J. Amer. Math. Soc. 21 (2008), no. 4, 1019--1063.pdf

  • [14] Merle, F; Raphael, P., Lower bound on the blow up rate of the critical norm for some radial $L^2$ super critical NLS equations, Amer. J. Math. 130 (2008), no. 4, 945--978.pdf

  • [13] Lemou, M.; Mehats, F.; Raphael, P., Structure of the linearized gravitational Vlasov-Poisson system close to a polytropic ground state. SIAM J. Math. Anal. 39 (2008), no. 6, 1711--1739.pdf

  • [12] Lemou, M.; Mehats, F.; Raphael, P., Uniqueness of the critical mass blow up solution for the four dimensional Vlasov-Poisson system, Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire 24 (2007), no. 5, 825--833.

  • [11] Lemou, M.; Mehats, F.; Raphael, P.,  The orbital stability of the ground states and the singularity formation for the gravitational Vlasov Poisson system, Arch. Ration. Mech. Anal. 189 (2008), no. 3, 425--468.

  • [10] Planchon, F.; Raphael, P., Existence and stability of the log-log blow up dynamics for the $L^2$ critical nonlinear Schr\"odinger equation in a domain, Ann. Henri Poincar\'e 8 (2007), no. 6, 1177--1219.pdf

  • [9] Raphael, P., Existence and stability of a solution blowing up on a sphere for a $L^2$ supercritical nonlinear Schr\"odinger equation, Duke Math. J. 134 (2), 199-258 (2006).pdf

  • [8] Fibich, G.; Merle, F.; Raphael, P., Numerical proof of a spectral property related to the singularity formation for the $L^2$ critical nonlinear Schr\"odinger equation,  Phys. D  220  (2006),  no. 1, 1--13. 

  • [7] Merle, F.; Raphael, P., On one blow up point solutions to the critical nonlinear Schr\"odinger equation, J. Hyperbolic Differ. Equ. 2 (2005), no. 4, 919--962. pdf

  • [6] Merle, F.; Raphael, P.,  Profiles and quantization of the blow up mass for critical nonlinear Schr\"odinger equation, Comm. Math. Phys.  253  (2005),  no. 3, 675--704. pdf

  • [5] Merle, F.; Raphael, P., Sharp lower bound on the blow up rate for critical nonlinear Schr\"odinger equation, J. Amer. Math. Soc. 19 (2006), no. 1, 37--90.pdf

  • [4] Raphael, P., Stability of the log-log bound for blow up solutions to the critical non linear Schr\"odinger equation,  Math. Ann.  331  (2005),  no. 3, 577--609.pdf

  • [3] Merle, F.; Rapha\"el, P., On universality of blow up profile for $L^2$ critical nonlinear Schr\"odinger equation, Invent. Math. 156, 565-672 (2004).pdf

  • [2] Merle, F.; Rapha\"el, P., Sharp upper bound on the blow up rate for critical nonlinear Schr\"odinger equation, Geom. Funct. Anal. 13 (2003), 591-642.pdf

  • [1] Merle, F.; Rapha\"el, P., Blow up dynamic and upper bound on the blow up rate for critical nonlinear Schr\"odinger equation, Ann. Math. 161 (2005), no. 1, 157--222. pdf