M. Keel

5.3k total citations · 3 hit papers
21 papers, 2.6k citations indexed

About

M. Keel is a scholar working on Mathematical Physics, Applied Mathematics and Control and Systems Engineering. According to data from OpenAlex, M. Keel has authored 21 papers receiving a total of 2.6k indexed citations (citations by other indexed papers that have themselves been cited), including 21 papers in Mathematical Physics, 10 papers in Applied Mathematics and 9 papers in Control and Systems Engineering. Recurrent topics in M. Keel's work include Advanced Mathematical Physics Problems (21 papers), Stability and Controllability of Differential Equations (9 papers) and Navier-Stokes equation solutions (7 papers). M. Keel is often cited by papers focused on Advanced Mathematical Physics Problems (21 papers), Stability and Controllability of Differential Equations (9 papers) and Navier-Stokes equation solutions (7 papers). M. Keel collaborates with scholars based in United States, Canada and Japan. M. Keel's co-authors include Terence Tao, J. Colliander, Hideo Takaoka, Gigliola Staffilani, Christopher D. Sogge, Hart F. Smith and T. Tao and has published in prestigious journals such as Annals of Mathematics, Communications on Pure and Applied Mathematics and Inventiones mathematicae.

In The Last Decade

M. Keel

21 papers receiving 2.2k citations

Hit Papers

align trajectories

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.

Endpoint Strichartz estimates

1998 1.0k citations M. Keel, Terence Tao American Journal of Mathematics profile →
Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋

2003 375 citations J. Colliander, M. Keel et al. Journal of the American Mathematical Society profile →
Global well-posedness and scattering for the energy-critical Schrödinger equation in ℝ³

2008 232 citations J. Colliander, M. Keel et al. Annals of Mathematics profile →

Peers — A (Enhanced Table)

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

Name	h						Papers	Cites
M. Keel United States	16	2.5k	1.3k	1.1k	568	128	21	2.6k
J. Colliander United States	24	2.2k 0.9×	993 0.8×	1.3k 1.2×	460 0.8×	114 0.9×	48	2.3k
Gigliola Staffilani United States	21	1.8k 0.7×	917 0.7×	876 0.8×	372 0.7×	94 0.7×	63	1.9k
Pierre Raphaël France	25	1.5k 0.6×	762 0.6×	792 0.8×	416 0.7×	62 0.5×	50	1.8k
Nakao Hayashi Japan	28	2.2k 0.9×	895 0.7×	1.0k 1.0×	625 1.1×	46 0.4×	139	2.3k
Manoussos G. Grillakis United States	19	2.2k 0.9×	480 0.4×	1.7k 1.6×	431 0.8×	71 0.6×	33	2.5k
Yvan Martel France	25	1.9k 0.8×	751 0.6×	1.4k 1.3×	488 0.9×	23 0.2×	61	2.5k
Luc Molinet France	27	1.8k 0.7×	849 0.6×	1.8k 1.7×	298 0.5×	18 0.1×	65	2.3k
Changxing Miao China	26	1.7k 0.7×	1.4k 1.1×	317 0.3×	522 0.9×	54 0.4×	103	1.9k
Pavel I. Naumkin Mexico	18	1.5k 0.6×	561 0.4×	774 0.7×	535 0.9×	21 0.2×	182	1.6k
Serge Alinhac France	20	1.1k 0.4×	1.0k 0.8×	245 0.2×	398 0.7×	96 0.8×	65	1.5k

Countries citing papers authored by M. Keel

Since Specialization

Citations

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

Fields of papers citing papers by M. Keel

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

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

Co-authorship network of co-authors of M. Keel

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

All Works

Sort: Min cites: Since: Top N: Style:

20 of 20 papers shown

Colliander, J., et al.. (2010). Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation. Inventiones mathematicae. 181(1). 39–113. 142 indexed citations

Colliander, J., M. Keel, Gigliola Staffilani, Hideo Takaoka, & Terence Tao. (2008). Global well-posedness and scattering for the energy-critical Schrödinger equation in ℝ³. Annals of Mathematics. 167(3). 767–865. 232 indexed citations breakdown →

Colliander, J., et al.. (2008). Resonant decompositions and the $I$-method for the cubic nonlinear Schrödinger equation on $\mathbb{R}^2$. Discrete and Continuous Dynamical Systems. 20(3). 665–686. 35 indexed citations

Colliander, J., Gigliola Staffilani, M. Keel, Hideo Takaoka, & Terence Tao. (2005). Symplectic nonsqueezing of the korteweg-de vries flow. Acta Mathematica. 195(2). 197–252. 15 indexed citations

Colliander, J., M. Keel, Gigliola Staffilani, Hideo Takaoka, & Terence Tao. (2004). Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on ℝ³. Communications on Pure and Applied Mathematics. 57(8). 987–1014. 118 indexed citations

Keel, M., Hart F. Smith, & Christopher D. Sogge. (2003). Almost global existence for quasilinear wave equations in three space dimensions. Journal of the American Mathematical Society. 17(1). 109–153. 58 indexed citations

Colliander, J., M. Keel, Gigliola Staffilani, Hideo Takaoka, & Terence Tao. (2003). Multilinear estimates for periodic KdV equations, and applications. Journal of Functional Analysis. 211(1). 173–218. 122 indexed citations

Colliander, J., M. Keel, Gigliola Staffilani, Hideo Takaoka, & Terence Tao. (2003). Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋. Journal of the American Mathematical Society. 16(3). 705–749. 375 indexed citations breakdown →

Colliander, J., M. Keel, Gigliola Staffilani, Hideo Takaoka, & Terence Tao. (2003). Polynomial upper bounds for the instability of the nonlinear Schrödinger equation below the energy norm. Communications on Pure & Applied Analysis. 2(1). 33–50. 7 indexed citations

10.

Colliander, J., M. Keel, Gigliola Staffilani, Hideo Takaoka, & Terence Tao. (2003). Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm. Discrete and Continuous Dynamical Systems. 9(1). 31–54. 19 indexed citations

11.

Keel, M., Hart F. Smith, & Christopher D. Sogge. (2002). Global Existence for a Quasilinear Wave Equation Outside of Star-Shaped Domains. Journal of Functional Analysis. 189(1). 155–226. 37 indexed citations

12.

Colliander, J., et al.. (2002). Existence globale et diffusion pour l’équation de Schrödinger non linéaire répulsive cubique sur m a t h b b R 3 en dessous l’espace d’énergie. Journées Équations aux dérivées partielles. 1–15. 2 indexed citations

13.

Colliander, J., et al.. (2002). A Refined Global Well-Posedness Result for Schrödinger Equations with Derivative. SIAM Journal on Mathematical Analysis. 34(1). 64–86. 106 indexed citations

14.

Colliander, J., M. Keel, Gigliola Staffilani, Hideo Takaoka, & Terence Tao. (2002). Almost Conservation Laws and Global Rough Solutions to a Nonlinear Schrödinger Equation. Mathematical Research Letters. 9(5). 659–682. 118 indexed citations

15.

Keel, M., Hart F. Smith, & Christopher D. Sogge. (2002). Almost global existence for some semilinear wave equations. Journal d Analyse Mathématique. 87(1). 265–279. 74 indexed citations

16.

Keel, M., Hart F. Smith, & Christopher D. Sogge. (2000). On global existence for nonlinear wave equations outside of convex obstacles. American Journal of Mathematics. 122(4). 805–842. 8 indexed citations

17.

Keel, M. & Terence Tao. (1999). Small data blow-up for semilinear Klein-Gordon equations. American Journal of Mathematics. 121(3). 629–669. 31 indexed citations

18.

Keel, M. & Terence Tao. (1998). . International Mathematics Research Notices. 1998(21). 1117–1117. 60 indexed citations

19.

Keel, M. & Terence Tao. (1998). Endpoint Strichartz estimates. American Journal of Mathematics. 120(5). 955–980. 1020 indexed citations breakdown →

20.

Keel, M.. (1995). Global existence for critical power Yang-Mills-Higgs equations. UMI eBooks. 1 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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