## Keel, Markus

Compute Distance To:
 Author ID: keel.markus Published as: Keel, Markus
 Documents Indexed: 26 Publications since 1997 Co-Authors: 12 Co-Authors with 25 Joint Publications 514 Co-Co-Authors
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### Co-Authors

 1 single-authored 18 Tao, Terence 15 Colliander, James E. 15 Staffilani, Gigliola 15 Takaoka, Hideo 4 Smith, Hart F. 4 Sogge, Christopher D. 1 Carleson, Lennart 1 Chang, Sun-Yung Alice 1 Jones, Peter Wilcox 1 Lax, Peter David 1 Rauch, Jeffrey B. 1 Roy, Tristan
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### Serials

 3 American Journal of Mathematics 3 Discrete and Continuous Dynamical Systems 2 Journal of Functional Analysis 2 Journal of the American Mathematical Society 2 SIAM Journal on Mathematical Analysis 1 Communications on Pure and Applied Mathematics 1 Journal d’Analyse Mathématique 1 Acta Mathematica 1 Inventiones Mathematicae 1 IMRN. International Mathematics Research Notices 1 Communications in Partial Differential Equations 1 Notices of the American Mathematical Society 1 Electronic Journal of Differential Equations (EJDE) 1 Mathematical Research Letters 1 Annals of Mathematics. Second Series 1 Communications on Pure and Applied Analysis
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### Fields

 25 Partial differential equations (35-XX) 8 Dynamical systems and ergodic theory (37-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Quantum theory (81-XX) 1 History and biography (01-XX) 1 Operator theory (47-XX) 1 Optics, electromagnetic theory (78-XX)

### Citations contained in zbMATH Open

24 Publications have been cited 2,020 times in 1,490 Documents Cited by Year
Endpoint Strichartz estimates. Zbl 0922.35028
Keel, Markus; Tao, Terence
1998
Sharp global well-posedness for KdV and modified KdV on $$\mathbb R$$ and $$\mathbb T$$. Zbl 1025.35025
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2003
Global well-posedness and scattering for the energy-critical Schrödinger equation in $$\mathbb R^{3}$$. Zbl 1178.35345
Colliander, James; Keel, Markus; Staffilani, Gigiola; Takaoka, Hideo; Tao, Terence
2008
Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation. Zbl 1197.35265
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence
2010
Multilinear estimates for periodic KdV equations, and applications. Zbl 1062.35109
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2004
A refined global well-posedness result for Schrödinger equations with derivative. Zbl 1034.35120
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2002
Global well-posedness for Schrödinger equations with derivative. Zbl 1002.35113
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2001
Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on $$\mathbb R^3$$. Zbl 1060.35131
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2004
Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation. Zbl 1152.35491
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2002
Almost global existence for some semilinear wave equations. Zbl 1031.35107
Keel, Markus; Smith, Hart F.; Sogge, Christopher D.
2002
Almost global existence for quasilinear wave equations in three space dimensions. Zbl 1055.35075
Keel, Markus; Smith, Hart F.; Sogge, Christopher D.
2004
Global well-posedness for KdV in Sobolev spaces of negative index. Zbl 0967.35119
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2001
Global existence for a quasilinear wave equation outside of star-shaped domains. Zbl 1001.35087
Keel, Markus; Smith, Hart F.; Sogge, Christopher D.
2002
Local and global well-posedness of wave maps on $$R^{1+1}$$ for rough data. Zbl 0999.58013
Keel, Markus; Tao, Terence
1998
Resonant decompositions and the $$I$$-method for the cubic nonlinear Schrödinger equation on $$\mathbb R^2$$. Zbl 1147.35095
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2008
Small data blow-up for semilinear Klein-Gordon equations. Zbl 0931.35105
Keel, Markus; Tao, Terence
1999
Global well-posedness of the Maxwell-Klein-Gordon equation below the energy norm. Zbl 1228.35241
Keel, Markus; Roy, Tristan; Tao, Terence
2011
Symplectic nonsqueezing of the Korteweg-de Vries flow. Zbl 1105.35104
Colliander, James; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo
2005
Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm. Zbl 1028.35141
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2003
Lectures on geometric optics. Zbl 0926.35003
Rauch, Jeffrey; Keel, Markus
1999
Global existence for critical power Yang-Mills-Higgs equations in $$\mathbb{R}^{3+1}$$. Zbl 0884.35134
Keel, Markus
1997
On global existence for nonlinear wave equations outside of convex obstacles. Zbl 0957.35088
Keel, Markus; Smith, Hart F.; Sogge, Christopher D.
2000
Polynomial upper bounds for the instability of the nonlinear Schrödinger equation below the energy norm. Zbl 1041.35070
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2003
The energy-critical nonlinear Schrödinger equation in $$\mathbb R^3$$. Zbl 1133.35091
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2007
Global well-posedness of the Maxwell-Klein-Gordon equation below the energy norm. Zbl 1228.35241
Keel, Markus; Roy, Tristan; Tao, Terence
2011
Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation. Zbl 1197.35265
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence
2010
Global well-posedness and scattering for the energy-critical Schrödinger equation in $$\mathbb R^{3}$$. Zbl 1178.35345
Colliander, James; Keel, Markus; Staffilani, Gigiola; Takaoka, Hideo; Tao, Terence
2008
Resonant decompositions and the $$I$$-method for the cubic nonlinear Schrödinger equation on $$\mathbb R^2$$. Zbl 1147.35095
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2008
The energy-critical nonlinear Schrödinger equation in $$\mathbb R^3$$. Zbl 1133.35091
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2007
Symplectic nonsqueezing of the Korteweg-de Vries flow. Zbl 1105.35104
Colliander, James; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo
2005
Multilinear estimates for periodic KdV equations, and applications. Zbl 1062.35109
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2004
Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on $$\mathbb R^3$$. Zbl 1060.35131
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2004
Almost global existence for quasilinear wave equations in three space dimensions. Zbl 1055.35075
Keel, Markus; Smith, Hart F.; Sogge, Christopher D.
2004
Sharp global well-posedness for KdV and modified KdV on $$\mathbb R$$ and $$\mathbb T$$. Zbl 1025.35025
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2003
Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm. Zbl 1028.35141
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2003
Polynomial upper bounds for the instability of the nonlinear Schrödinger equation below the energy norm. Zbl 1041.35070
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2003
A refined global well-posedness result for Schrödinger equations with derivative. Zbl 1034.35120
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2002
Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation. Zbl 1152.35491
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2002
Almost global existence for some semilinear wave equations. Zbl 1031.35107
Keel, Markus; Smith, Hart F.; Sogge, Christopher D.
2002
Global existence for a quasilinear wave equation outside of star-shaped domains. Zbl 1001.35087
Keel, Markus; Smith, Hart F.; Sogge, Christopher D.
2002
Global well-posedness for Schrödinger equations with derivative. Zbl 1002.35113
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2001
Global well-posedness for KdV in Sobolev spaces of negative index. Zbl 0967.35119
Colliander, James E.; Keel, Markus; Staffilani, Gigliola; Takaoka, Hideo; Tao, Terence C.
2001
On global existence for nonlinear wave equations outside of convex obstacles. Zbl 0957.35088
Keel, Markus; Smith, Hart F.; Sogge, Christopher D.
2000
Small data blow-up for semilinear Klein-Gordon equations. Zbl 0931.35105
Keel, Markus; Tao, Terence
1999
Lectures on geometric optics. Zbl 0926.35003
Rauch, Jeffrey; Keel, Markus
1999
Endpoint Strichartz estimates. Zbl 0922.35028
Keel, Markus; Tao, Terence
1998
Local and global well-posedness of wave maps on $$R^{1+1}$$ for rough data. Zbl 0999.58013
Keel, Markus; Tao, Terence
1998
Global existence for critical power Yang-Mills-Higgs equations in $$\mathbb{R}^{3+1}$$. Zbl 0884.35134
Keel, Markus
1997
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### Cited by 1,141 Authors

 29 Oh, Tadahiro 27 Miao, Changxing 26 Zheng, Jiqiang 24 Himonas, A. Alexandrou 23 Zhang, Junyong 20 Lee, Sanghyuk 20 Seo, Ihyeok 20 Visan, Monica 19 Guo, Zihua 19 Metcalfe, Jason L. 18 Carles, Rémi 17 Sogge, Christopher D. 17 Staffilani, Gigliola 17 Tao, Terence 17 Tataru, Daniel 16 Dinh, Van Duong 16 Hong, Younghun 16 Killip, Rowan 16 Tzvetkov, Nikolay 16 Wang, Chengbo 16 Xu, Guixiang 16 Yan, Wei 16 Zhang, Xiaoyi 15 Li, Yongsheng 14 Murphy, Jason 14 Schippa, Robert 14 Visciglia, Nicola 14 Wang, Baoxiang 14 Wang, Yuzhao 13 Ozawa, Tohru 12 Antonelli, Paolo 12 Colliander, James E. 12 Dodson, Benjamin G. 12 Fang, Daoyuan 12 Herr, Sebastian 12 Koh, Youngwoo 12 Mizutani, Haruya 12 Nakanishi, Kenji 12 Zhao, Lifeng 11 Cho, Yonggeun 11 D’Ancona, Piero 11 Hidano, Kunio 11 Hoshino, Gaku 11 Pausader, Benoît 11 Zhang, Bingyu 10 Beceanu, Marius 10 Fanelli, Luca 10 Kenig, Carlos Eduardo 10 Kwak, Chulkwang 10 Li, Pingrun 10 Saanouni, Tarek 9 Bez, Neal 9 Hani, Zaher 9 Ionescu, Alexandru D. 9 Kappeler, Thomas 9 Linares, Felipe 9 Marcati, Pierangelo 9 Petronilho, Gerson 9 Pierfelice, Vittoria 9 Pocovnicu, Oana 9 Ponce, Gustavo 9 Procesi, Michela 9 Smith, Hart F. 9 Stefanov, Atanas G. 9 Tesfahun, Achenef 8 Germain, Pierre 8 Holmer, Justin 8 Ikeda, Masahiro 8 Selberg, Sigmund 8 Soffer, Avraham 8 Takaoka, Hideo 8 Tzirakis, Nikolaos 8 Zha, Dongbing 8 Zhao, Zehua 7 Carvajal, Xavier Paredes 7 Corcho, Adán J. 7 Gerard, Patrick 7 Guo, Boling 7 Han, Wei 7 Hirayama, Hiroyuki 7 Huang, Jianhua 7 Keel, Markus 7 Li, Dong 7 Panthee, Mahendra 7 Planchon, Fabrice 7 Roy, Tristan 7 Sun, Shuming 7 Thomann, Laurent 7 Tohaneanu, Mihai 7 Vega, Luis 7 Wang, Ming 7 Yan, Fangchi 7 Yang, Kai 7 Yao, Xiaohua 6 Alazard, Thomas 6 Blair, Matthew D. 6 Chen, Gong 6 Chen, Jiecheng 6 Chen, Xuwen 6 Cui, Shangbin ...and 1,041 more Authors
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### Cited in 215 Serials

 113 Journal of Differential Equations 88 Journal of Mathematical Analysis and Applications 78 Communications in Partial Differential Equations 68 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 61 Communications in Mathematical Physics 59 Journal of Functional Analysis 46 Discrete and Continuous Dynamical Systems 35 Transactions of the American Mathematical Society 35 Communications on Pure and Applied Analysis 33 Proceedings of the American Mathematical Society 31 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 30 Journal of Mathematical Physics 27 Journal of Hyperbolic Differential Equations 25 Advances in Mathematics 25 SIAM Journal on Mathematical Analysis 22 Archive for Rational Mechanics and Analysis 22 Journal of Evolution Equations 21 Journal de Mathématiques Pures et Appliquées. Neuvième Série 21 NoDEA. Nonlinear Differential Equations and Applications 20 Mathematische Annalen 18 Communications in Contemporary Mathematics 17 Analysis & PDE 16 Acta Mathematica Sinica. English Series 14 Journal d’Analyse Mathématique 14 Revista Matemática Iberoamericana 12 Communications on Pure and Applied Mathematics 11 Applicable Analysis 11 Mathematical Methods in the Applied Sciences 11 Duke Mathematical Journal 11 Journal of Dynamics and Differential Equations 11 The Journal of Fourier Analysis and Applications 10 Science China. Mathematics 9 Nonlinearity 9 The Journal of Geometric Analysis 9 Journal of the European Mathematical Society (JEMS) 9 Annales Henri Poincaré 9 Annals of PDE 9 Séminaire Laurent Schwartz. EDP et Applications 8 Inventiones Mathematicae 8 Physica D 8 Journal of the American Mathematical Society 8 Forum Mathematicum 8 Comptes Rendus. Mathématique. Académie des Sciences, Paris 8 Pure and Applied Analysis 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Mathematische Zeitschrift 7 Nonlinear Analysis. Real World Applications 7 Stochastic and Partial Differential Equations. Analysis and Computations 6 Memoirs of the American Mathematical Society 6 Journal of Nonlinear Science 6 SN Partial Differential Equations and Applications 5 Annales de l’Institut Fourier 5 Archiv der Mathematik 5 Journal of Computational and Applied Mathematics 5 Quarterly of Applied Mathematics 5 Bulletin of the American Mathematical Society. New Series 5 Calculus of Variations and Partial Differential Equations 5 Abstract and Applied Analysis 5 Bulletin of the Brazilian Mathematical Society. New Series 5 Discrete and Continuous Dynamical Systems. Series S 5 Forum of Mathematics, Sigma 4 Letters in Mathematical Physics 4 Journal of the Mathematical Society of Japan 4 Chinese Annals of Mathematics. Series B 4 Acta Applicandae Mathematicae 4 Selecta Mathematica. New Series 4 Mathematical Physics, Analysis and Geometry 4 Journal of Inequalities and Applications 4 Boundary Value Problems 4 Analysis and Mathematical Physics 3 Reviews in Mathematical Physics 3 American Journal of Mathematics 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Indiana University Mathematics Journal 3 Manuscripta Mathematica 3 Mathematische Nachrichten 3 Monatshefte für Mathematik 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Acta Mathematicae Applicatae Sinica. English Series 3 Applied Mathematics Letters 3 Journal of Scientific Computing 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 Geometric and Functional Analysis. GAFA 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Analysis (München) 3 Communications in Nonlinear Science and Numerical Simulation 3 Differential Equations 3 Analysis in Theory and Applications 3 Journal of Pseudo-Differential Operators and Applications 3 Journal of Spectral Theory 3 Forum of Mathematics, Pi 3 Evolution Equations and Control Theory 2 Mathematics of Computation 2 Acta Mathematica 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Bulletin de la Société Mathématique de France 2 Illinois Journal of Mathematics 2 Nagoya Mathematical Journal 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 SIAM Journal on Numerical Analysis ...and 115 more Serials
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### Cited in 41 Fields

 1,433 Partial differential equations (35-XX) 156 Dynamical systems and ergodic theory (37-XX) 145 Quantum theory (81-XX) 124 Harmonic analysis on Euclidean spaces (42-XX) 94 Fluid mechanics (76-XX) 93 Operator theory (47-XX) 70 Global analysis, analysis on manifolds (58-XX) 47 Statistical mechanics, structure of matter (82-XX) 43 Functional analysis (46-XX) 43 Optics, electromagnetic theory (78-XX) 38 Numerical analysis (65-XX) 33 Probability theory and stochastic processes (60-XX) 18 Ordinary differential equations (34-XX) 16 Relativity and gravitational theory (83-XX) 15 Differential geometry (53-XX) 14 Topological groups, Lie groups (22-XX) 14 Integral equations (45-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 11 Real functions (26-XX) 11 Abstract harmonic analysis (43-XX) 10 Mechanics of deformable solids (74-XX) 9 Functions of a complex variable (30-XX) 9 Mechanics of particles and systems (70-XX) 8 Difference and functional equations (39-XX) 8 Systems theory; control (93-XX) 6 Measure and integration (28-XX) 6 Special functions (33-XX) 6 Approximations and expansions (41-XX) 4 Combinatorics (05-XX) 3 Number theory (11-XX) 3 Integral transforms, operational calculus (44-XX) 3 Geophysics (86-XX) 2 Potential theory (31-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Statistics (62-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 Convex and discrete geometry (52-XX) 1 Classical thermodynamics, heat transfer (80-XX)