P. Raphaël

发表

A Two-Soliton with Transient Turbulent Regime for the Cubic Half-Wave Equation on the Real Line

P. Gérard, E. Lenzmann, Oana Pocovnicu, 2016, 1611.08482.

Uniqueness of the critical mass blow up solution for the four dimensional gravitational Vlasov-Poisson system

M. Lemou, F. Méhats, P. Raphaël, 2007 .

Y. Martel, P. Raphaël, Yakine Bahri, 2019, Annales Henri Poincaré.

N ov 2 01 9 SELF-SIMILAR BLOW-UP PROFILES FOR SLIGHTLY SUPERCRITICAL NONLINEAR SCHRÖDINGER EQUATIONS

Y. Martel, P. Raphaël, Yakine Bahri, 2019 .

F. Merle, J. Szeftel, P. Raphaël, 2009, 0907.4098.

O C ] 2 0 A pr 2 02 2 Regularity in shape optimization under convexity constraint

P. Raphaël, L. Jimmy, Amboley, 2022 .

On small traveling waves to the mass critical fractional NLS

I. Naumkin, P. Raphaël, 2018, Calculus of Variations and Partial Differential Equations.

Orbital stability of spherical galactic models

M. Lemou, F. Méhats, P. Raphaël, 2011, Inventiones mathematicae.

Dynamics Near the Ground State for the Energy Critical Nonlinear Heat Equation in Large Dimensions

Charles Collot, P. Raphaël, F. Merle, 2016, Communications in Mathematical Physics.

Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems

I. Rodnianski, P. Raphaël, 2009, Publications mathématiques de l'IHÉS.

The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation

Pierre Raphaël, Frank Merle, F. Merle, 2005 .

Blow up of the critical norm for some radial L2 super critical nonlinear Schrödinger equations

P. Raphaël, F. Merle, 2006, math/0605378.

On the stability of critical chemotactic aggregation

P. Raphaël, Rémi Schweyer, 2012, 1209.2517.

Blow up for the critical generalized Korteweg–de Vries equation. I: Dynamics near the soliton

F. Merle, Y. Martel, P. Raphaël, 2014 .

Two‐soliton solutions to the three‐dimensional gravitational Hartree equation

Joachim Krieger, Yvan Martel, Y. Martel, 2008, 0811.3637.

Strongly interacting blow up bubbles for the mass critical nonlinear Schrödinger equation

Y. Martel, P. Raphaël, 2018 .

The instability of Bourgain-Wang solutions for the L2 critical NLS

J. Szeftel, P. Raphaël, F. Merle, 2010, 1010.5168.

Structure of the Linearized Gravitational Vlasov-Poisson System Close to a Polytropic Ground State

Mohammed Lemou, Florian Méhats, Pierre Raphaël, 2008, SIAM J. Math. Anal..

Dynamics Near the Ground State for the Energy Critical Nonlinear Heat Equation in Large Dimensions

F. Merle, Charles Collot, P. Raphaël, 2016, 1604.08323.

Near soliton dynamics and singularity formation for critical problems

F. Merle, Pierre Raphael, Y. Martel, 2014, 1412.2375.

Blow up and near soliton dynamics for the $L^2$ critical gKdV equation

F. Merle, Y. Martel, P. Raphaël, 2011 .

On Traveling Waves of the Nonlinear Schrödinger Equation Escaping a Potential Well

I. Naumkin, P. Raphaël, 2018, Annales Henri Poincaré.

Proof of a Spectral Property related to the singularity formation for the L2 critical nonlinear Schrödinger equation

Gadi Fibich, Pierre Raphaël, Frank Merle, 2006 .

Stable Blowup Dynamics for the 1‐Corotational Energy Critical Harmonic Heat Flow

P. Raphaël, Rémi Schweyer, 2011, 1106.0914.

Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem

Pierre Raphaël, Frank Merle, Igor Rodnianski, 2013 .

Standing Ring Blow up Solutions to the N-Dimensional Quintic Nonlinear Schrödinger Equation

J. Szeftel, P. Raphaël, 2009 .

Codimension One Threshold Manifold for the Critical gKdV Equation

F. Merle, K. Nakanishi, Y. Martel, 2015, 1502.04594.

Nondispersive solutions to the L2-critical Half-Wave Equation

E. Lenzmann, J. Krieger, P. Raphaël, 2013, Archive for Rational Mechanics and Analysis.

Nondispersive solutions to the L2-critical Half-Wave Equation

E. Lenzmann, J. Krieger, P. Raphaël, 2012, 1203.2476.

On Stability of Pseudo-Conformal Blowup for L2-critical Hartree NLS

E. Lenzmann, J. Krieger, P. Raphaël, 2008, 0808.2324.

Existence and stability of a solution blowing up on a sphere for a L 2 supercritical non linear Schrödinger equation

P. Raphaël, 2008 .

Existence and Stability of the log–log Blow-up Dynamics for the L2-Critical Nonlinear Schrödinger Equation in a Domain

F. Planchon, P. Raphaël, 2007 .

ON ONE BLOW UP POINT SOLUTIONS TO THE CRITICAL NONLINEAR SCHRÖDINGER EQUATION

F. Merle, P. Raphaël, 2005 .

Stability of the log-log bound for blow up solutions to the critical non linear Schrödinger equation

Pierre Raphaël, P. Raphaël, 2005 .

On the blow up phenomenon for the L 2 critical nonlinear Schrödinger Equation

P. Raphaël, 2004 .

Y. Martel, P. Raphaël, Yakine Bahri, 2021, Annales Henri Poincaré.

ON THE TRANSVERSAL STABILITY OF SELF SIMILAR BLOW UP FOR THE ENERGY SUPER CRITICAL HEAT EQUATION

F. Merle, J. Szeftel, P. Raphaël, 2016 .

Codimension One Threshold Manifold for the Critical gKdV Equation

F. Merle, K. Nakanishi, Y. Martel, 2015, Communications in Mathematical Physics.

Orbital stability of spherical galactic models

M. Lemou, F. Méhats, P. Raphaël, 2010, Inventiones mathematicae.

A New Variational Approach to the Stability of Gravitational Systems

M. Lemou, F. Méhats, P. Raphaël, 2009, 0904.2443.

ON MELTING AND FREEZING FOR THE 2 D RADIAL STEFAN

P. Raphaël, 2017 .

M. Lemou, F. Méhats, P. Raphaël, 2007 .

On blow up for the energy super critical defocusing nonlinear Schrödinger equations

F. Merle, J. Szeftel, I. Rodnianski, 2019, Inventiones mathematicae.

On collapsing ring blow up solutions to the mass supercritical NLS

F. Merle, J. Szeftel, P. Raphaël, 2014 .

On blow up for the energy super critical defocusing nonlinear Schrödinger equations

J. Szeftel, I. Rodnianski, P. Raphaël, 2021, Inventiones mathematicae.

On the implosion of a compressible fluid I: Smooth self-similar inviscid profiles

F. Merle, J. Szeftel, I. Rodnianski, 2022, Annals of Mathematics.

On the implosion of a compressible fluid II: Singularity formation

F. Merle, J. Szeftel, I. Rodnianski, 2022, Annals of Mathematics.

Stability of ODE blow-up for the energy critical semilinear heat equation

F. Merle, Charles Collot, P. Raphaël, 2017 .

Rough blowup solutions to the L2 critical NLS

J. Colliander, P. Raphaël, 2009 .

The instability of Bourgain-Wang solutions for the L2 critical NLS

J. Szeftel, P. Raphaël, F. Merle, 2010, 1010.5168.