Edit Profile (opens in new tab) Holmer, Justin Compute Distance To: Compute Author ID: holmer.justin Published as: Holmer, Justin; Holmer, J. External Links: MGP Documents Indexed: 42 Publications since 2005 Co-Authors: 22 Co-Authors with 38 Joint Publications 597 Co-Co-Authors all top 5 Co-Authors 4 single-authored 13 Roudenko, Svetlana 8 Chen, Xuwen 6 Zworski, Maciej 4 Farah, Luiz Gustavo 2 Colliander, James E. 2 Liu, Chang 2 Marzuola, Jeremy L. 2 Perelman, Galina 2 Tataru, Daniel 2 Tzirakis, Nikolaos 1 Adami, Riccardo 1 Bejenaru, Ioan 1 Christ, Michael 1 Datchev, Kiril R. 1 Duyckaerts, Thomas 1 Fukuizumi, Reika 1 Herr, Sebastian 1 Lin, Quanhui 1 Platte, Rodrigo B. 1 Visan, Monica 1 Zhang, Katherine Zhiyuan 1 Zhang, Xiaoyi all top 5 Serials 4 IMRN. International Mathematics Research Notices 3 Communications in Mathematical Physics 3 Nonlinearity 3 Transactions of the American Mathematical Society 3 Communications in Partial Differential Equations 2 Archive for Rational Mechanics and Analysis 2 Communications on Pure and Applied Analysis 2 AMRX. Applied Mathematics Research eXpress 2 Journal of Hyperbolic Differential Equations 2 Analysis & PDE 1 Journal of Mathematical Analysis and Applications 1 Inventiones Mathematicae 1 Differential and Integral Equations 1 SIAM Journal on Mathematical Analysis 1 Journal of Nonlinear Science 1 Electronic Journal of Differential Equations (EJDE) 1 Mathematical Research Letters 1 Journal of the European Mathematical Society (JEMS) 1 Journal of Modern Dynamics 1 São Paulo Journal of Mathematical Sciences 1 Forum of Mathematics, Pi 1 Libertas Mathematica. New Series all top 5 Fields 42 Partial differential equations (35-XX) 16 Dynamical systems and ergodic theory (37-XX) 11 Quantum theory (81-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Special functions (33-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 39 Publications have been cited 877 times in 523 Documents Cited by ▼ Year ▼ A sharp condition for scattering of the radial 3D cubic nonlinear Schrödinger equation. Zbl 1155.35094Holmer, Justin; Roudenko, Svetlana 103 2008 Scattering for the nonradial 3D cubic nonlinear Schrödinger equation. Zbl 1171.35472Duyckaerts, Thomas; Holmer, Justin; Roudenko, Svetlana 95 2008 The initial-boundary value problem for the Korteweg–de Vries equation. Zbl 1111.35062Holmer, Justin 69 2006 On the 2D Zakharov system with \(L^{2}\) Schrödinger data. Zbl 1173.35651Bejenaru, I.; Herr, S.; Holmer, J.; Tataru, D. 56 2009 The initial-boundary-value problem for the 1D nonlinear Schrödinger equation on the half-line. Zbl 1212.35448Holmer, Justin 55 2005 Fast soliton scattering by delta impurities. Zbl 1126.35068Holmer, Justin; Marzuola, Jeremy; Zworski, Maciej 44 2007 Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems. Zbl 1158.35085Colliander, James; Holmer, Justin; Tzirakis, Nikolaos 40 2008 Focusing quantum many-body dynamics: the rigorous derivation of the 1D focusing cubic nonlinear Schrödinger equation. Zbl 1338.35407Chen, Xuwen; Holmer, Justin 38 2016 On blow-up solutions to the 3D cubic nonlinear Schrödinger equation. Zbl 1130.35361Holmer, Justin; Roudenko, Svetlana 31 2007 Slow solution interaction with delta imperiums. Zbl 1137.35060Holmer, Justin; Zworski, Maciej 31 2007 Soliton splitting by external delta potentials. Zbl 1128.35384Holmer, J.; Marzuola, J.; Zworski, M. 28 2007 On the Klainerman-Machedon conjecture for the quantum BBGKY hierarchy with self-interaction. Zbl 1342.35322Chen, Xuwen; Holmer, Justin 26 2016 On the rigorous derivation of the 2D cubic nonlinear Schrödinger equation from 3D quantum many-body dynamics. Zbl 1288.35429Chen, Xuwen; Holmer, Justin 25 2013 Correlation structures, many-body scattering processes, and the derivation of the Gross-Pitaevskii hierarchy. Zbl 1404.35407Chen, Xuwen; Holmer, Justin 23 2016 Soliton interaction with slowly varying potentials. Zbl 1147.35084Holmer, Justin; Zworski, Maciej 21 2008 Local ill-posedness of the 1D Zakharov system. Zbl 1115.35124Holmer, Justin 17 2007 Divergence of infinite-variance nonradial solutions to the 3d NLS equation. Zbl 1195.35277Holmer, Justin; Roudenko, Svetlana 17 2010 Focusing quantum many-body dynamics. II: The rigorous derivation of the 1D focusing cubic nonlinear Schrödinger equation from 3D. Zbl 1368.35245Chen, Xuwen; Holmer, Justin 17 2017 The rigorous derivation of the 2D cubic focusing NLS from quantum many-body evolution. Zbl 1405.81029Chen, Xuwen; Holmer, Justin 16 2017 Fast soliton scattering by attractive delta impurities. Zbl 1194.35403Datchev, Kiril; Holmer, Justin 15 2009 Low regularity a priori bounds for the modified Korteweg-de Vries equation. Zbl 1284.35367Christ, Michael; Holmer, Justin; Tataru, Daniel 14 2012 The derivation of the \(\mathbb{T}^{3}\) energy-critical NLS from quantum many-body dynamics. Zbl 1422.35148Chen, Xuwen; Holmer, Justin 12 2019 Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on \(\mathbb R\). Zbl 1157.35103Colliander, James; Holmer, Justin; Visan, Monica; Zhang, Xiaoyi 11 2008 Effective dynamics of double solitons for perturbed mKdV. Zbl 1300.37046Holmer, Justin; Perelman, Galina; Zworski, Maciej 10 2011 Blow-up criteria for the 3D cubic nonlinear Schrödinger equation. Zbl 1202.37105Holmer, Justin; Platte, Rodrigo; Roudenko, Svetlana 10 2010 Dynamics of KdV solitons in the presence of a slowly varying potential. Zbl 1247.35132Holmer, Justin 7 2011 Breathing patterns in nonlinear relaxation. Zbl 1173.35685Holmer, Justin; Zworski, Maciej 7 2009 Instability of solitons – revisited. II: The supercritical Zakharov-Kuznetsov equation. Zbl 1423.35337Farah, Luiz Gustavo; Holmer, Justin; Roudenko, Svetlana 6 2019 Blow-up for the 1D nonlinear Schrödinger equation with point nonlinearity. I: Basic theory. Zbl 1436.35290Holmer, Justin; Liu, Chang 5 2020 Phase-driven interaction of widely separated nonlinear Schrödinger solitons. Zbl 1256.35137Holmer, Justin; Lin, Quanhui 4 2012 Instability of solitons – revisited. I: The critical generalized KdV equation. Zbl 1423.35336Farah, Luiz Gustavo; Holmer, Justin; Roudenko, Svetlana 4 2019 Blow-up solutions on a sphere for the 3D quintic NLS in the energy space. Zbl 1329.35280Holmer, Justin; Roudenko, Svetlana 3 2012 A class of solutions to the 3D cubic nonlinear Schrödinger equation that blows up on a circle. Zbl 1220.35159Holmer, Justin; Roudenko, Svetlana 3 2011 Asymptotically linear solutions in \(H^{1}\) of the 2-D defocusing nonlinear Schrödinger and Hartree equations. Zbl 1188.35179Holmer, Justin; Tzirakis, Nikolaos 3 2010 Instability of solitons in the 2D cubic Zakharov-Kuznetsov equation. Zbl 1440.35267Farah, Luiz Gustavo; Holmer, Justin; Roudenko, Svetlana 3 2019 On instability of solitons in the 2d cubic Zakharov-Kuznetsov equation. Zbl 1431.35153Farah, Luiz Gustavo; Holmer, Justin; Roudenko, Svetlana 3 2019 A solution to the focusing 3d NLS that blows up on a contracting sphere. Zbl 1325.35201Holmer, Justin; Perelman, Galina; Roudenko, Svetlana 2 2015 Scattering for the \(L^2\) supercritical point NLS. Zbl 1457.35064Adami, Riccardo; Fukuizumi, Reika; Holmer, Justin 2 2021 Blow-up for the 1D nonlinear Schrödinger equation with point nonlinearity. II: Supercritical blow-up profiles. Zbl 1460.35328Holmer, Justin; Liu, Chang 1 2021 Scattering for the \(L^2\) supercritical point NLS. Zbl 1457.35064Adami, Riccardo; Fukuizumi, Reika; Holmer, Justin 2 2021 Blow-up for the 1D nonlinear Schrödinger equation with point nonlinearity. II: Supercritical blow-up profiles. Zbl 1460.35328Holmer, Justin; Liu, Chang 1 2021 Blow-up for the 1D nonlinear Schrödinger equation with point nonlinearity. I: Basic theory. Zbl 1436.35290Holmer, Justin; Liu, Chang 5 2020 The derivation of the \(\mathbb{T}^{3}\) energy-critical NLS from quantum many-body dynamics. Zbl 1422.35148Chen, Xuwen; Holmer, Justin 12 2019 Instability of solitons – revisited. II: The supercritical Zakharov-Kuznetsov equation. Zbl 1423.35337Farah, Luiz Gustavo; Holmer, Justin; Roudenko, Svetlana 6 2019 Instability of solitons – revisited. I: The critical generalized KdV equation. Zbl 1423.35336Farah, Luiz Gustavo; Holmer, Justin; Roudenko, Svetlana 4 2019 Instability of solitons in the 2D cubic Zakharov-Kuznetsov equation. Zbl 1440.35267Farah, Luiz Gustavo; Holmer, Justin; Roudenko, Svetlana 3 2019 On instability of solitons in the 2d cubic Zakharov-Kuznetsov equation. Zbl 1431.35153Farah, Luiz Gustavo; Holmer, Justin; Roudenko, Svetlana 3 2019 Focusing quantum many-body dynamics. II: The rigorous derivation of the 1D focusing cubic nonlinear Schrödinger equation from 3D. Zbl 1368.35245Chen, Xuwen; Holmer, Justin 17 2017 The rigorous derivation of the 2D cubic focusing NLS from quantum many-body evolution. Zbl 1405.81029Chen, Xuwen; Holmer, Justin 16 2017 Focusing quantum many-body dynamics: the rigorous derivation of the 1D focusing cubic nonlinear Schrödinger equation. Zbl 1338.35407Chen, Xuwen; Holmer, Justin 38 2016 On the Klainerman-Machedon conjecture for the quantum BBGKY hierarchy with self-interaction. Zbl 1342.35322Chen, Xuwen; Holmer, Justin 26 2016 Correlation structures, many-body scattering processes, and the derivation of the Gross-Pitaevskii hierarchy. Zbl 1404.35407Chen, Xuwen; Holmer, Justin 23 2016 A solution to the focusing 3d NLS that blows up on a contracting sphere. Zbl 1325.35201Holmer, Justin; Perelman, Galina; Roudenko, Svetlana 2 2015 On the rigorous derivation of the 2D cubic nonlinear Schrödinger equation from 3D quantum many-body dynamics. Zbl 1288.35429Chen, Xuwen; Holmer, Justin 25 2013 Low regularity a priori bounds for the modified Korteweg-de Vries equation. Zbl 1284.35367Christ, Michael; Holmer, Justin; Tataru, Daniel 14 2012 Phase-driven interaction of widely separated nonlinear Schrödinger solitons. Zbl 1256.35137Holmer, Justin; Lin, Quanhui 4 2012 Blow-up solutions on a sphere for the 3D quintic NLS in the energy space. Zbl 1329.35280Holmer, Justin; Roudenko, Svetlana 3 2012 Effective dynamics of double solitons for perturbed mKdV. Zbl 1300.37046Holmer, Justin; Perelman, Galina; Zworski, Maciej 10 2011 Dynamics of KdV solitons in the presence of a slowly varying potential. Zbl 1247.35132Holmer, Justin 7 2011 A class of solutions to the 3D cubic nonlinear Schrödinger equation that blows up on a circle. Zbl 1220.35159Holmer, Justin; Roudenko, Svetlana 3 2011 Divergence of infinite-variance nonradial solutions to the 3d NLS equation. Zbl 1195.35277Holmer, Justin; Roudenko, Svetlana 17 2010 Blow-up criteria for the 3D cubic nonlinear Schrödinger equation. Zbl 1202.37105Holmer, Justin; Platte, Rodrigo; Roudenko, Svetlana 10 2010 Asymptotically linear solutions in \(H^{1}\) of the 2-D defocusing nonlinear Schrödinger and Hartree equations. Zbl 1188.35179Holmer, Justin; Tzirakis, Nikolaos 3 2010 On the 2D Zakharov system with \(L^{2}\) Schrödinger data. Zbl 1173.35651Bejenaru, I.; Herr, S.; Holmer, J.; Tataru, D. 56 2009 Fast soliton scattering by attractive delta impurities. Zbl 1194.35403Datchev, Kiril; Holmer, Justin 15 2009 Breathing patterns in nonlinear relaxation. Zbl 1173.35685Holmer, Justin; Zworski, Maciej 7 2009 A sharp condition for scattering of the radial 3D cubic nonlinear Schrödinger equation. Zbl 1155.35094Holmer, Justin; Roudenko, Svetlana 103 2008 Scattering for the nonradial 3D cubic nonlinear Schrödinger equation. Zbl 1171.35472Duyckaerts, Thomas; Holmer, Justin; Roudenko, Svetlana 95 2008 Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems. Zbl 1158.35085Colliander, James; Holmer, Justin; Tzirakis, Nikolaos 40 2008 Soliton interaction with slowly varying potentials. Zbl 1147.35084Holmer, Justin; Zworski, Maciej 21 2008 Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on \(\mathbb R\). Zbl 1157.35103Colliander, James; Holmer, Justin; Visan, Monica; Zhang, Xiaoyi 11 2008 Fast soliton scattering by delta impurities. Zbl 1126.35068Holmer, Justin; Marzuola, Jeremy; Zworski, Maciej 44 2007 On blow-up solutions to the 3D cubic nonlinear Schrödinger equation. Zbl 1130.35361Holmer, Justin; Roudenko, Svetlana 31 2007 Slow solution interaction with delta imperiums. Zbl 1137.35060Holmer, Justin; Zworski, Maciej 31 2007 Soliton splitting by external delta potentials. Zbl 1128.35384Holmer, J.; Marzuola, J.; Zworski, M. 28 2007 Local ill-posedness of the 1D Zakharov system. Zbl 1115.35124Holmer, Justin 17 2007 The initial-boundary value problem for the Korteweg–de Vries equation. Zbl 1111.35062Holmer, Justin 69 2006 The initial-boundary-value problem for the 1D nonlinear Schrödinger equation on the half-line. Zbl 1212.35448Holmer, Justin 55 2005 all cited Publications top 5 cited Publications all top 5 Cited by 521 Authors 20 Holmer, Justin 17 Roudenko, Svetlana 16 Zhang, Bingyu 14 Guo, Boling 13 Kaikina, Elena Igorevna 12 Farah, Luiz Gustavo 11 Murphy, Jason 9 Dinh, Van Duong 9 Saanouni, Tarek 9 Sun, Shuming 8 Cavalcante, Márcio André Araújo 8 Himonas, A. Alexandrou 8 Miao, Changxing 8 Tzirakis, Nikolaos 7 Grillakis, Manoussos G. 7 Hayashi, Nakao 7 Hong, Younghun 7 Pastor, Ademir 7 Schlein, Benjamin 7 Staffilani, Gigliola 7 Zhang, Jingjun 6 Angulo Pava, Jaime 6 Duyckaerts, Thomas 6 Guo, Yanfeng 6 Kinoshita, Shinya 6 Machedon, Matei 6 Maeda, Masaya 6 Mantzavinos, Dionyssios 6 Merle, Frank 6 Muñoz, Claudio 6 Pavlović, Nataša 6 Phan Thành Nam 6 Pokhozhaev, Stanislav I. 6 Schippa, Robert 6 Soffer, Avraham 6 Sohinger, Vedran 5 Akahori, Takafumi 5 Chen, Thomas M. 5 Chen, Xuwen 5 Cuccagna, Scipio 5 Fang, Yung-Fu 5 Forcella, Luigi 5 Gao, Yanfang 5 Guo, Qing 5 Guzmán, Carlos M. 5 Herr, Sebastian 5 Ikeda, Masahiro 5 Marzuola, Jeremy L. 5 Nakanishi, Kenji 5 Oh, Tadahiro 5 Ozawa, Tohru 5 Pecher, Hartmut 5 Yan, Fangchi 5 Yang, Kai 5 You, Shujun 5 Zhu, Shihui 4 Adami, Riccardo 4 Bennett, Jonathan M. 4 Bez, Neal 4 Bona, Jerry Lloyd 4 Boßmann, Lea 4 Colliander, James E. 4 Compaan, Erin 4 Fang, Daoyuan 4 Kenig, Carlos Eduardo 4 Kikuchi, Hiroaki 4 Kishimoto, Nobu 4 Li, Donglong 4 Linares, Felipe 4 Ning, Xiaoqi 4 Noja, Diego 4 Rougerie, Nicolas 4 Wang, Zhiyong 4 Zheng, Jiqiang 3 Alejo, Miguel A. 3 Hernandez Ardila, Alex 3 Beceanu, Marius 3 Brennecke, Christian 3 Campos, Luccas 3 Cardoso, Mykael 3 Carles, Rémi 3 Corcho, Adán J. 3 Deng, Qingquan 3 Dodson, Benjamin G. 3 Esquivel, Liliana 3 Fukuizumi, Reika 3 Glass, Olivier 3 Guerrero, Sergio 3 Hamano, Masaru 3 Hirayama, Hiroyuki 3 Ibrahim, Slim 3 Inui, Takahisa 3 Killip, Rowan 3 Kwak, Chulkwang 3 Kwon, Soonsik 3 Le Coz, Stefan 3 Li, Shenghao 3 Lu, Jing 3 Mashkin, Timur 3 Nawa, Hayato ...and 421 more Authors all top 5 Cited in 134 Serials 37 Journal of Differential Equations 26 Journal of Mathematical Physics 25 Communications in Mathematical Physics 23 Journal of Mathematical Analysis and Applications 19 Journal of Functional Analysis 19 Discrete and Continuous Dynamical Systems 19 Communications on Pure and Applied Analysis 17 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 14 Communications in Partial Differential Equations 13 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 11 Transactions of the American Mathematical Society 11 SIAM Journal on Mathematical Analysis 10 Archive for Rational Mechanics and Analysis 10 Physica D 10 Journal of Evolution Equations 9 Nonlinearity 9 ZAMP. Zeitschrift für angewandte Mathematik und Physik 9 Proceedings of the American Mathematical Society 9 Annales Henri Poincaré 8 NoDEA. Nonlinear Differential Equations and Applications 8 Journal of Hyperbolic Differential Equations 6 Communications on Pure and Applied Mathematics 6 Letters in Mathematical Physics 6 Revista Matemática Iberoamericana 6 Discrete and Continuous Dynamical Systems. Series S 4 Reviews in Mathematical Physics 4 Quarterly of Applied Mathematics 4 Journal of Nonlinear Science 4 Calculus of Variations and Partial Differential Equations 4 Journal of Inequalities and Applications 4 Communications in Contemporary Mathematics 4 Nonlinear Analysis. Real World Applications 4 Analysis & PDE 3 Advances in Mathematics 3 Duke Mathematical Journal 3 Indiana University Mathematics Journal 3 Applied Mathematics Letters 3 Journal of Scientific Computing 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Acta Mathematica Sinica. English Series 3 Differential Equations 3 Bulletin of the Brazilian Mathematical Society. New Series 3 Advances in Difference Equations 3 Boundary Value Problems 3 São Paulo Journal of Mathematical Sciences 3 Science China. Mathematics 2 Applicable Analysis 2 Journal of Computational Physics 2 Illinois Journal of Mathematics 2 Mathematische Annalen 2 Monatshefte für Mathematik 2 Chinese Annals of Mathematics. Series B 2 Applied Numerical Mathematics 2 Acta Mathematicae Applicatae Sinica. English Series 2 The Journal of Geometric Analysis 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Taiwanese Journal of Mathematics 2 Kyoto Journal of Mathematics 2 Mathematical Control and Related Fields 2 SN Partial Differential Equations and Applications 1 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 Journal d’Analyse Mathématique 1 Journal of Statistical Physics 1 Mathematical Methods in the Applied Sciences 1 Mathematical Notes 1 Theoretical and Mathematical Physics 1 Wave Motion 1 Mathematics of Computation 1 Annales de l’Institut Fourier 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Archiv der Mathematik 1 BIT 1 Functional Analysis and its Applications 1 Inventiones Mathematicae 1 Journal of Computational and Applied Mathematics 1 Manuscripta Mathematica 1 Mathematics and Computers in Simulation 1 Mathematische Nachrichten 1 Memoirs of the American Mathematical Society 1 Quaestiones Mathematicae 1 Studies in Applied Mathematics 1 Systems & Control Letters 1 Applied Mathematics and Mechanics. (English Edition) 1 Acta Applicandae Mathematicae 1 Asymptotic Analysis 1 MCSS. Mathematics of Control, Signals, and Systems 1 Applications of Mathematics 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 Geometric and Functional Analysis. GAFA 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Journal of Mathematical Sciences (New York) 1 Kyushu Journal of Mathematics 1 Selecta Mathematica. New Series 1 Opuscula Mathematica 1 Nonlinear Dynamics 1 Mathematical Physics, Analysis and Geometry 1 Chaos ...and 34 more Serials all top 5 Cited in 31 Fields 510 Partial differential equations (35-XX) 88 Quantum theory (81-XX) 57 Dynamical systems and ergodic theory (37-XX) 46 Statistical mechanics, structure of matter (82-XX) 23 Numerical analysis (65-XX) 22 Fluid mechanics (76-XX) 15 Harmonic analysis on Euclidean spaces (42-XX) 14 Systems theory; control (93-XX) 13 Operator theory (47-XX) 13 Optics, electromagnetic theory (78-XX) 10 Ordinary differential equations (34-XX) 9 Integral transforms, operational calculus (44-XX) 8 Probability theory and stochastic processes (60-XX) 7 Functional analysis (46-XX) 6 Real functions (26-XX) 4 Potential theory (31-XX) 4 Mechanics of particles and systems (70-XX) 3 Integral equations (45-XX) 3 Differential geometry (53-XX) 2 Measure and integration (28-XX) 2 Special functions (33-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Convex and discrete geometry (52-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Associative rings and algebras (16-XX) 1 Approximations and expansions (41-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) Citations by Year