Frank Merle

8.6k total citations · 1 hit paper
98 papers, 4.6k citations indexed

About

Frank Merle is a scholar working on Mathematical Physics, Statistical and Nonlinear Physics and Control and Systems Engineering. According to data from OpenAlex, Frank Merle has authored 98 papers receiving a total of 4.6k indexed citations (citations by other indexed papers that have themselves been cited), including 91 papers in Mathematical Physics, 45 papers in Statistical and Nonlinear Physics and 40 papers in Control and Systems Engineering. Recurrent topics in Frank Merle's work include Advanced Mathematical Physics Problems (90 papers), Nonlinear Waves and Solitons (41 papers) and Stability and Controllability of Differential Equations (40 papers). Frank Merle is often cited by papers focused on Advanced Mathematical Physics Problems (90 papers), Nonlinear Waves and Solitons (41 papers) and Stability and Controllability of Differential Equations (40 papers). Frank Merle collaborates with scholars based in France, United States and Japan. Frank Merle's co-authors include Pierre Raphaël, Yvan Martel, Carlos E. Kenig, Hatem Zaag, Haı̈m Brezis, Thomas Duyckaerts, Yoshio Tsutsumi, Tai‐Peng Tsai, Hiroshi Matano and Jérémie Szeftel 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

Frank Merle

96 papers receiving 4.1k citations

Hit Papers

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What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation

2008 242 citations Carlos E. Kenig, Frank Merle profile →

Peers

Countries citing papers authored by Frank Merle

Since Specialization

Citations

This map shows the geographic impact of Frank Merle'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 Frank Merle with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Frank Merle more than expected).

Fields of papers citing papers by Frank Merle

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Frank Merle. 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 Frank Merle. The network helps show where Frank Merle may publish in the future.

Co-authorship network of co-authors of Frank Merle

This figure shows the co-authorship network connecting the top 25 collaborators of Frank Merle. A scholar is included among the top collaborators of Frank Merle 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 Frank Merle. Frank Merle is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

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20 of 20 papers shown

#	Work	Indexed citations
1	On degenerate blow-up profiles for the subcritical semilinear heat equation 2024 ·Journal of the European Mathematical Society ·Frank Merle, Hatem Zaag	0
2	Decay estimates for nonradiative solutions of the energy-critical\n focusing wave equation 2019 ·arXiv (Cornell University) ·Thomas Duyckaerts, Carlos E. Kenig, Frank Merle	9
3	Strongly anisotropic type II blow up at an isolated point 2019 ·Journal of the American Mathematical Society ·(unknown), Frank Merle, Pierre Raphaël	8
4	Universality of blow up profile for small blow up solutions to the\n energy critical wave map equation 2016 ·arXiv (Cornell University) ·Thomas Duyckaerts, Hao Jia, Carlos E. Kenig, Frank Merle	10
5	Scattering profile for global solutions of the energy-critical wave\n equation 2016 ·arXiv (Cornell University) ·Thomas Duyckaerts, Carlos E. Kenig, Frank Merle	12
6	Concentration-compactness and universal profiles for the non-radial\n energy critical wave equation 2015 ·arXiv (Cornell University) ·Thomas Duyckaerts, Carlos E. Kenig, Frank Merle	9
7	Solutions of the focusing nonradial critical wave equation with the\n compactness property 2014 ·arXiv (Cornell University) ·Thomas Duyckaerts, Carlos E. Kenig, Frank Merle	22
8	Profiles for bounded solutions of dispersive equations, with\n applications to energy-critical wave and Schr\\"odinger equations 2013 ·arXiv (Cornell University) ·Frank Merle, Thomas Duyckaerts, Carlos E. Kenig	13
9	Classification of radial solutions of the focusing, energy-critical wave equation 2013 ·HAL (Le Centre pour la Communication Scientifique Directe) ·Frank Merle, Carlos E. Kenig, Thomas Duyckaerts	86
10	Blow-up behavior outside the origin for a semilinear wave equation in the radial case 2011 ·Bulletin des Sciences Mathématiques ·Frank Merle, Hatem Zaag	15
11	Threshold and generic type I behaviors for a supercritical nonlinear heat equation 2011 ·Journal of Functional Analysis ·Hiroshi Matano, Frank Merle	35
12	Universality of the blow-up profile for small type II blow-up solutions\n of energy-critical wave equation: the non-radial case 2010 ·arXiv (Cornell University) ·Thomas Duyckaerts, Carlos E. Kenig, Frank Merle	64
13	Scattering for Ḣ^{1/2} bounded solutions to the cubic, defocusing NLS in 3 dimensions 2009 ·Transactions of the American Mathematical Society ·Carlos E. Kenig, Frank Merle	65
14	Blow up of the critical norm for some radial L 2 super critical nonlinear Schrödinger equations 2008 ·American Journal of Mathematics ·Frank Merle, Pierre Raphaël	34
15	Classification of type I and type II behaviors for a supercritical nonlinear heat equation 2008 ·Journal of Functional Analysis ·Hiroshi Matano, Frank Merle	66
16	On the energy critical focusing non-linear wave equation 2007 ·French digital mathematics library (Numdam) ·Carlos E. Kenig, Frank Merle	2
17	Multi solitary waves for nonlinear Schrödinger equations 2006 ·Annales de l Institut Henri Poincaré C Analyse Non Linéaire ·Yvan Martel, Frank Merle	65
18	On a sharp lower bound on the blow-up rate for the 𝐿² critical nonlinear Schrödinger equation 2005 ·Journal of the American Mathematical Society ·Frank Merle, Pierre Raphaël	97
19	L2 concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity 1990 ·Journal of Differential Equations ·Frank Merle, Yoshio Tsutsumi	129
20	Existence of excited states for a nonlinear Dirac field 1988 ·Communications in Mathematical Physics ·Mikhaël Balabane, Thierry Cazenave, Adrien Douady, Frank Merle	59

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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