Pierre Raphael

Mathematical Physics · 2003–2014

A researcher in the Science corpus: 13 papers; trusts 19 researchers and is trusted by 40 researchers here, as inferred from the citation graph.

Subfields

• Mathematical Physics — 91 citations into it; #265 of 8,562 by trust here, #226 by citations
• Statistical and Nonlinear Physics — 67 citations into it; #639 of 10,127 by trust here, #1,166 by citations
• Applied Mathematics — 50 citations into it; #6,283 of 7,620 by trust here, #5,443 by citations
• Control and Systems Engineering — 13 citations into it; #771 of 8,257 by trust here, #1,718 by citations
• Atomic and Molecular Physics, and Optics — 5 citations into it

Whom Pierre Raphael trusts overall

Their strongest outbound trust, strongest first, inferred from their citations.

1. F. Merle
2. Yvan Martel
3. Carlos E. Kenig
4. Thomas Duyckaerts
5. Igor Rodnianski
6. Gadi Fibich
7. J. Krieger
8. D. Tataru
9. Catherine Sulem
10. Nicolas Burq

Who trusts Pierre Raphael overall

1. F. Merle
2. Yvan Martel
3. Hatem Zaag
4. F. Planchon
5. Carlos E. Kenig
6. Carlos M. Guzm'an
7. Jérémie Szeftel
8. Thomas Duyckaerts
9. Terence Tao
10. Hao Jia

Papers from Pierre Raphael's perspective

Ordered by how strongly the researchers Pierre Raphael trusts endorse each paper. Same corpus, a different order for every researcher.

1. Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case
2. Renormalization and blow up for charge one equivariant critical wave maps
3. Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation
4. A Liouville theorem for the critical generalized Korteweg–de Vries equation
5. Semilinear Schrodinger Equations
6. Two singular dynamics of the nonlinear Schrödinger equation on a plane domain
7. Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation
8. Multi solitary waves for nonlinear Schrödinger equations
9. Asymptotic N-soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations
10. The nonlinear Schrödinger equation : self-focusing and wave collapse

Their papers

• Blow up for the critical generalized Korteweg–de Vries equation. I: Dynamics near the soliton (2014) — 117 citations
• Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem (2013) — 120 citations
• Blow up for the critical gKdV equation III: exotic regimes (2012) — 58 citations
• On collapsing ring blow up solutions to the mass supercritical NLS (2012) — 50 citations
• Blow up for the critical gKdV equation II: minimal mass dynamics (2012) — 65 citations
• Existence and uniqueness of minimal blow-up solutions to an inhomogeneous mass critical NLS (2010) — 143 citations
• Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems (2009) — 221 citations
• Existence and Stability of the log–log Blow-up Dynamics for the L2-Critical Nonlinear Schrödinger Equation in a Domain (2007) — 49 citations
• Proof of a Spectral Property related to the singularity formation for the L2 critical nonlinear Schrödinger equation (2006) — 73 citations
• The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation (2005) — 373 citations
• Profiles and Quantization of the Blow Up Mass for Critical Nonlinear Schrödinger Equation (2005) — 215 citations
• On universality of blow-up profile for L2 critical nonlinear Schrödinger equation (2004) — 300 citations
• Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation (2003) — 259 citations