Pierre Raphaël

3.6k citations

50 papers · 1.8k indexed · h-index 25

Impact in

Mathematical Physics top 0.5%
- Advanced Mathematical Physics Problems
- Spectral Theory in Mathematical Physics
- advanced mathematical theories
Applied Mathematics top 0.5%
- Navier-Stokes equation solutions
- Nonlinear Partial Differential Equations

Papers in ⓘ

Mathematical Physics 47
- Advanced Mathematical Physics Problems 46
- Spectral Theory in Mathematical Physics 9
Applied Mathematics 26
- Navier-Stokes equation solutions 17
- Nonlinear Partial Differential Equations 10
- Gas Dynamics and Kinetic Theory 8

Co-authors: Frank Merle (22 shared papers)Jérémie Szeftel (10 shared papers)Igor Rodnianski (6 shared papers)Yvan Martel (6 shared papers)Florian Méhats (9 shared papers)Mohammed Lemou (9 shared papers)Joachim Krieger (2 shared papers)Enno Lenzmann (2 shared papers)
Journals: Journal of the American Mathematical Society (4 papers)Comptes Rendus Mathématique (3 papers)Inventiones mathematicae (3 papers)Mathematische Annalen (3 papers)Annals of Mathematics (3 papers)
Partner nations: France United States United Kingdom

In The Last Decade

Pierre Raphaël

49 papers receiving 1.6k citations

Peers

Countries citing papers authored by Pierre Raphaël

Since Specialization

Citations

This map shows the geographic impact of Pierre Raphaël's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Pierre Raphaël with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Pierre Raphaël more than expected).

Fields of papers citing papers by Pierre Raphaël

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Pierre Raphaël. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Pierre Raphaël. The network helps show where Pierre Raphaël may publish in the future.

Co-authors

The 15 scholars most cited alongside Pierre Raphaël, linked wherever they have co-authored with each other. Click a name or a connecting line to browse the papers they share.

Border = papers with Pierre Raphaël Line = papers co-authored together Pierre Raphaël links everyone, so they are left out of the graph.

All Works

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20 of 20 papers shown

Showing the 20 most-cited of 50 papers — load more, or switch the sort, to bring in the rest.

#	Work
1	The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation Annals of Mathematics ·Frank Merle, Pierre Raphaël	2005	178
2	On universality of blow-up profile for L 2 critical nonlinear Schr�dinger equation Inventiones mathematicae ·Frank Merle, Pierre Raphaël	2004	145
3	Sharp upper bound on the blow-up rate for the critical nonlinear Schr�dinger equation Geometric and Functional Analysis ·Frank Merle, Pierre Raphaël	2003	143
4	Profiles and Quantization of the Blow Up Mass for Critical Nonlinear Schr�dinger Equation Communications in Mathematical Physics ·Frank Merle, Pierre Raphaël	2004	106
5	On a sharp lower bound on the blow-up rate for the 𝐿² critical nonlinear Schrödinger equation Journal of the American Mathematical Society ·Frank Merle, Pierre Raphaël	2005	97
6	Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems Publications mathématiques de l IHÉS ·Pierre Raphaël, Igor Rodnianski	2012	93
7	Existence and uniqueness of minimal blow-up solutions to an inhomogeneous mass critical NLS Journal of the American Mathematical Society ·Pierre Raphaël, Jérémie Szeftel	2010	75
8	Nondispersive solutions to the L 2-critical Half-Wave Equation Archive for Rational Mechanics and Analysis ·Joachim Krieger, Enno Lenzmann, Pierre Raphaël	2013	63
9	Stability of the log-log bound for blow up solutions to the critical non linear Schr�dinger equation Mathematische Annalen ·Pierre Raphaël	2005	57
10	Blow up for the critical generalized Korteweg–de Vries equation. I: Dynamics near the soliton Acta Mathematica ·Yvan Martel, Frank Merle, Pierre Raphaël	2014	57
11	Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem Inventiones mathematicae ·Frank Merle, Pierre Raphaël, Igor Rodnianski	2012	51
12	Stable blow up dynamics for the 1-corotational energy critical harmonic\n heat flow arXiv (Cornell University) ·Pierre Raphaël, Rémi Schweyer	2011	44
13	Smooth type II blow-up solutions to the four-dimensional energy-critical wave equation Analysis & PDE ·Matthieu Hillairet, Pierre Raphaël	2012	43
14	On the stability of critical chemotactic aggregation Mathematische Annalen ·Pierre Raphaël, Rémi Schweyer	2013	40
15	Proof of a Spectral Property related to the singularity formation for the critical nonlinear Schrödinger equation Physica D Nonlinear Phenomena ·Gadi Fibich, Frank Merle, Pierre Raphaël	2006	36
16	Blow up of the critical norm for some radial L 2 super critical nonlinear Schrödinger equations American Journal of Mathematics ·Frank Merle, Pierre Raphaël	2008	34
17	On the implosion of a compressible fluid I: Smooth self-similar inviscid profiles Annals of Mathematics ·Frank Merle, Pierre Raphaël, Igor Rodnianski, Jérémie Szeftel	2022	34
18	Two‐soliton solutions to the three‐dimensional gravitational Hartree equation Communications on Pure and Applied Mathematics ·Joachim Krieger, Pierre Raphaël, Yvan Martel	2009	33
19	Orbital stability of spherical galactic models Inventiones mathematicae ·Mohammed Lemou, Florian Méhats, Pierre Raphaël	2011	33
20	On the implosion of a compressible fluid II: Singularity formation Annals of Mathematics ·Frank Merle, Pierre Raphaël, Igor Rodnianski, Jérémie Szeftel	2022	32

About Pierre Raphaël

Pierre Raphaël is a scholar working on Mathematical Physics, Applied Mathematics, Statistical and Nonlinear Physics, Control and Systems Engineering and Nuclear and High Energy Physics, having authored 50 papers that have together received 1.8k indexed citations. Recurring topics across this work include Advanced Mathematical Physics Problems (46 papers), Navier-Stokes equation solutions (17 papers), Nonlinear Waves and Solitons (15 papers), Stability and Controllability of Differential Equations (14 papers), Nonlinear Partial Differential Equations (10 papers), Spectral Theory in Mathematical Physics (9 papers), Gas Dynamics and Kinetic Theory (8 papers) and Nonlinear Photonic Systems (7 papers). The work is most often cited by research in Mathematical Physics (1.5k citations), Applied Mathematics (762 citations), Statistical and Nonlinear Physics (792 citations), Modeling and Simulation (101 citations) and Control and Systems Engineering (416 citations). Pierre Raphaël has collaborated with scholars based in France, United States and United Kingdom. Frequent co-authors include Frank Merle, Jérémie Szeftel, Igor Rodnianski, Yvan Martel, Florian Méhats, Mohammed Lemou, Joachim Krieger, Enno Lenzmann, Matthieu Hillairet and Fabrice Planchon. Their work appears in journals such as Journal of the American Mathematical Society, Comptes Rendus Mathématique, Inventiones mathematicae, Mathematische Annalen and Annals of Mathematics.

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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