Pierre Raphaël

3.6k total citations
50 papers, 1.8k citations indexed

About

Pierre Raphaël is a scholar working on Mathematical Physics, Applied Mathematics and Statistical and Nonlinear Physics. According to data from OpenAlex, Pierre Raphaël has authored 50 papers receiving a total of 1.8k indexed citations (citations by other indexed papers that have themselves been cited), including 47 papers in Mathematical Physics, 26 papers in Applied Mathematics and 18 papers in Statistical and Nonlinear Physics. Recurrent topics in Pierre Raphaël's work include Advanced Mathematical Physics Problems (46 papers), Navier-Stokes equation solutions (17 papers) and Nonlinear Waves and Solitons (15 papers). Pierre Raphaël is often cited by papers focused on Advanced Mathematical Physics Problems (46 papers), Navier-Stokes equation solutions (17 papers) and Nonlinear Waves and Solitons (15 papers). Pierre Raphaël collaborates with scholars based in France, United States and United Kingdom. Pierre Raphaël's co-authors include Frank Merle, Jérémie Szeftel, Igor Rodnianski, Yvan Martel, Florian Méhats, Mohammed Lemou, Joachim Krieger, Enno Lenzmann, Matthieu Hillairet and Gadi Fibich and has published in prestigious journals such as Communications in Mathematical Physics, Annals of Mathematics and Communications on Pure and Applied Mathematics.

In The Last Decade

Pierre Raphaël

49 papers receiving 1.6k citations

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name h Career Trend Papers Cites
Pierre Raphaël France 25 1.5k 792 762 416 122 50 1.8k
Luc Molinet France 27 1.8k 1.2× 1.8k 2.2× 849 1.1× 298 0.7× 94 0.8× 65 2.3k
Yvan Martel France 25 1.9k 1.3× 1.4k 1.8× 751 1.0× 488 1.2× 67 0.5× 61 2.5k
J. Colliander United States 24 2.2k 1.4× 1.3k 1.6× 993 1.3× 460 1.1× 119 1.0× 48 2.3k
Nakao Hayashi Japan 28 2.2k 1.4× 1.0k 1.3× 895 1.2× 625 1.5× 33 0.3× 139 2.3k
A. Alexandrou Himonas United States 26 1.6k 1.1× 1.7k 2.1× 679 0.9× 125 0.3× 69 0.6× 98 2.2k
M. Keel United States 16 2.5k 1.6× 1.1k 1.3× 1.3k 1.7× 568 1.4× 98 0.8× 21 2.6k
Gerard Misiołek United States 19 778 0.5× 1.0k 1.3× 418 0.5× 88 0.2× 69 0.6× 39 1.4k
Zhaoyang Yin China 29 2.3k 1.5× 3.2k 4.1× 935 1.2× 227 0.5× 121 1.0× 174 3.6k
Jean-Marc Delort France 17 775 0.5× 492 0.6× 408 0.5× 219 0.5× 200 1.6× 46 1.1k
Albert Fathi France 20 609 0.4× 568 0.7× 449 0.6× 87 0.2× 36 0.3× 47 1.3k

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-authorship network of co-authors of Pierre Raphaël

This figure shows the co-authorship network connecting the top 25 collaborators of Pierre Raphaël. A scholar is included among the top collaborators of Pierre Raphaël based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Pierre Raphaël. Pierre Raphaël is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

20 of 20 papers shown
1.
Merle, Frank, et al.. (2019). Strongly anisotropic type II blow up at an isolated point. Journal of the American Mathematical Society. 33(2). 527–607. 8 indexed citations
2.
Raphaël, Pierre, et al.. (2018). On small traveling waves to the mass critical fractional NLS. Calculus of Variations and Partial Differential Equations. 57(3). 5 indexed citations
3.
Merle, Frank, Pierre Raphaël, & Jérémie Szeftel. (2018). On Strongly Anisotropic Type I Blowup. International Mathematics Research Notices. 9 indexed citations
4.
Merle, Frank, et al.. (2016). Stability of ODE blow-up for the energy critical semilinear heat equation. Comptes Rendus Mathématique. 355(1). 65–79. 4 indexed citations
5.
Coz, Stefan Le, Yvan Martel, & Pierre Raphaël. (2014). Minimal mass blow up solutions for a double power nonlinear\n Schr\\"odinger equation. arXiv (Cornell University). 24 indexed citations
6.
Martel, Yvan, Frank Merle, & Pierre Raphaël. (2014). Blow up and near soliton dynamics for the L 2 critical gKdV equation. French digital mathematics library (Numdam). 1–14. 1 indexed citations
7.
Raphaël, Pierre, et al.. (2013). On the stability of critical chemotactic aggregation. Mathematische Annalen. 359(1-2). 267–377. 40 indexed citations
8.
Raphaël, Pierre, et al.. (2011). Stable blow up dynamics for the 1-corotational energy critical harmonic\n heat flow. arXiv (Cornell University). 44 indexed citations
9.
Lemou, Mohammed, Florian Méhats, & Pierre Raphaël. (2009). A new variational approach to the stability of gravitational systems. Comptes Rendus Mathématique. 347(15-16). 979–984.
10.
Lemou, Mohammed, Florian Méhats, & Pierre Raphaël. (2009). Stable Ground States for the Relativistic Gravitational Vlasov–Poisson System. Communications in Partial Differential Equations. 34(7). 703–721. 5 indexed citations
11.
Raphaël, Pierre & Jérémie Szeftel. (2009). Standing Ring Blow up Solutions to the N-Dimensional Quintic Nonlinear Schrödinger Equation. Communications in Mathematical Physics. 290(3). 973–996. 18 indexed citations
12.
Merle, Frank & Pierre Raphaël. (2008). Blow up of the critical norm for some radial L 2 super critical nonlinear Schrödinger equations. American Journal of Mathematics. 130(4). 945–978. 34 indexed citations
13.
Lemou, Mohammed, Florian Méhats, & Pierre Raphaël. (2008). The Orbital Stability of the Ground States and the Singularity Formation for the Gravitational Vlasov Poisson System. Archive for Rational Mechanics and Analysis. 189(3). 425–468. 23 indexed citations
14.
Lemou, Mohammed, Florian Méhats, & Pierre Raphaël. (2007). Stable self-similar blow up dynamics for the three dimensional relativistic gravitational Vlasov-Poisson system. Journal of the American Mathematical Society. 21(4). 1019–1063. 12 indexed citations
15.
Fibich, Gadi, Frank Merle, & Pierre Raphaël. (2006). Proof of a Spectral Property related to the singularity formation for the critical nonlinear Schrödinger equation. Physica D Nonlinear Phenomena. 220(1). 1–13. 36 indexed citations
16.
Merle, Frank & Pierre Raphaël. (2005). On a sharp lower bound on the blow-up rate for the 𝐿² critical nonlinear Schrödinger equation. Journal of the American Mathematical Society. 19(1). 37–90. 97 indexed citations
17.
Lemou, Mohammed, Florian Méhats, & Pierre Raphaël. (2005). Orbital stability and singularity formation for Vlasov–Poisson systems. Comptes Rendus Mathématique. 341(4). 269–274. 11 indexed citations
18.
Merle, Frank & Pierre Raphaël. (2005). ON ONE BLOW UP POINT SOLUTIONS TO THE CRITICAL NONLINEAR SCHRÖDINGER EQUATION. Journal of Hyperbolic Differential Equations. 2(4). 919–962. 11 indexed citations
19.
Merle, Frank & Pierre Raphaël. (2004). On universality of blow-up profile for L 2 critical nonlinear Schr�dinger equation. Inventiones mathematicae. 156(3). 565–672. 145 indexed citations
20.
Merle, Frank & Pierre Raphaël. (2002). Blow up dynamic and upper bound on the blow up rate for critical nonlinear Schrödinger equation. Journées Équations aux dérivées partielles. 1–5. 5 indexed citations

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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