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Raphaël Pierre
Raphaël Pierre
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The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation
F Merle, P Raphael
Annals of mathematics, 157-222, 2005
3902005
On universality of blow-up profile for L 2 critical nonlinear Schrödinger equation
F Merle, P Raphael
Inventiones mathematicae 156, 565-672, 2004
3322004
On a sharp lower bound on the blow-up rate for the 𝐿² critical nonlinear Schrödinger equation
F Merle, P Raphael
Journal of the American Mathematical Society 19 (1), 37-90, 2006
2522006
Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems
P Raphaël, I Rodnianski
Publications mathématiques de l'IHÉS 115, 1-122, 2012
2312012
Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation
F Merle, P Raphael
Communications in mathematical physics 253, 675-704, 2005
2282005
Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation
F Merle, P Raphael
Geometric & Functional Analysis GAFA 13, 591-642, 2003
2282003
Existence and uniqueness of minimal blow-up solutions to an inhomogeneous mass critical NLS
P Raphaël, J Szeftel
Journal of the American Mathematical Society 24 (2), 471-546, 2011
1522011
Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem
F Merle, P Raphaël, I Rodnianski
Inventiones mathematicae 193, 249-365, 2013
1312013
Stable blowup dynamics for the 1‐corotational energy critical harmonic heat flow
P Raphaël, R Schweyer
Communications on Pure and Applied Mathematics 66 (3), 414-480, 2013
1232013
Stability of the log-log bound for blow up solutions to the critical non linear Schrödinger equation
P Raphael
Mathematische Annalen 331, 577-609, 2005
1222005
Nondispersive solutions to the L 2-critical half-wave equation
J Krieger, E Lenzmann, P Raphaël
Archive for rational mechanics and analysis 209 (1), 61-129, 2013
1172013
Blow up for the critical generalized Korteweg–de Vries equation. I: Dynamics near the soliton
Y Martel, F Merle, P Raphaël
1122014
Smooth type II blow-up solutions to the four-dimensional energy-critical wave equation
M Hillairet, P Raphaël
Anal. PDE 5 (4), 777-829, 2012
902012
On the stability of critical chemotactic aggregation
P Raphaël, R Schweyer
Mathematische Annalen 359, 267-377, 2014
862014
Orbital stability of spherical galactic models
M Lemou, F Méhats, P Raphaël
Inventiones mathematicae 187, 145-194, 2012
792012
Two‐soliton solutions to the three‐dimensional gravitational Hartree equation
J Krieger, P Raphaël, Y Martel
Communications on Pure and Applied Mathematics: A Journal Issued by the …, 2009
742009
Strongly interacting blow up bubbles for the mass critical NLS
Y Martel, P Raphaël
722018
Proof of a spectral property related to the singularity formation for the L2 critical nonlinear Schrödinger equation
G Fibich, F Merle, P Raphaël
Physica D: Nonlinear Phenomena 220 (1), 1-13, 2006
722006
Quantized slow blow-up dynamics for the corotational energy-critical harmonic heat flow
P Raphaël, R Schweyer
Analysis & PDE 7 (8), 1713-1805, 2015
712015
Blow up for the critical gKdV equation III: exotic regimes
Y Martel, F Merle, P Raphaël
arXiv preprint arXiv:1209.2510, 2012
712012
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