Edit Profile (opens in new tab) Klainerman, Sergiu Compute Distance To: Compute Author ID: klainerman.sergiu Published as: Klainerman, Sergiu; Klainerman, S. Homepage: https://web.math.princeton.edu/~seri/homepage/seri.htm External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 103 Publications since 1980, including 3 Books 3 Contributions as Editor · 1 Further Contribution Co-Authors: 30 Co-Authors with 73 Joint Publications 1,279 Co-Co-Authors all top 5 Co-Authors 33 single-authored 22 Rodnianski, Igor 13 Machedon, Matei 8 Ionescu, Alexandru D. 7 Szeftel, Jérémie 4 Christodoulou, Demetrios 4 Nicolò, Francesco 3 Alexakis, Spyros 3 Majda, Andrew J. 2 Bourgain, Jean 2 Foschi, Damiano 2 Selberg, Sigmund 2 Tataru, Daniel 1 Agmon, Shmuel 1 Andersson, Lars Åke 1 Bahri, Abbas 1 Ben-Artzi, Matania 1 Berestycki, Henri 1 Birindelli, Isabeau 1 Brézis, Haïm 1 Caffarelli, Luis Ángel 1 Chang, Kung-Ching 1 Chang, Sun-Yung Alice 1 Guedes de Figueiredo, Djairo 1 Ekeland, Ivar 1 Fefferman, Charles Louis 1 Galloway, Gregory J. 1 Holzegel, Gustav 1 John, Fritz 1 Kenig, Carlos Eduardo 1 Kinderlehrer, David 1 Kohn, Joseph J. 1 Kohn, Robert Vita 1 Lax, Peter David 1 Li, YanYan 1 Lin, Fang Hua 1 Luk, Jonathan 1 Ni, Wei-Ming 1 Ponce, Gustavo 1 Rabinowitz, Paul Henry 1 Sarnak, Peter Clive 1 Shatah, Jalal 1 Sideris, Thomas C. 1 Speck, Jared 1 Staffilani, Gigliola 1 Tao, Terence 1 Tarantello, Gabriella 1 Tian, Gang 1 Varadhan, S. R. Srinivasa 1 Vogelius, Michael S. 1 Wang, Qian 1 Wong, Willie Wai-Yeung 1 Yang, Shiwu 1 Yau, Shing-Tung all top 5 Serials 17 Communications on Pure and Applied Mathematics 6 IMRN. International Mathematics Research Notices 5 Duke Mathematical Journal 5 Journal of Hyperbolic Differential Equations 4 Inventiones Mathematicae 4 Journal of the American Mathematical Society 3 Classical and Quantum Gravity 3 Communications in Mathematical Physics 3 Geometric and Functional Analysis. GAFA 3 Annals of Mathematics. Second Series 3 Annals of PDE 2 Journal d’Analyse Mathématique 2 Séminaire Équations aux Dérivées Partielles 2 Annals of Mathematics Studies 1 Archive for Rational Mechanics and Analysis 1 Acta Mathematica 1 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Differential and Integral Equations 1 Communications in Partial Differential Equations 1 Bulletin of the American Mathematical Society. New Series 1 Notices of the American Mathematical Society 1 International Journal of Modern Physics D 1 Discrete and Continuous Dynamical Systems 1 Journal of the European Mathematical Society (JEMS) 1 Communications in Contemporary Mathematics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Communications on Pure and Applied Analysis 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Contemporary Mathematics 1 Princeton Mathematical Series 1 Progress in Mathematical Physics 1 Séminaire Laurent Schwartz. EDP et Applications all top 5 Fields 90 Partial differential equations (35-XX) 47 Relativity and gravitational theory (83-XX) 24 Differential geometry (53-XX) 18 Global analysis, analysis on manifolds (58-XX) 7 Quantum theory (81-XX) 6 Functional analysis (46-XX) 4 Fluid mechanics (76-XX) 3 General and overarching topics; collections (00-XX) 3 History and biography (01-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 90 Publications have been cited 3,877 times in 2,142 Documents Cited by ▼ Year ▼ Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. Zbl 0476.76068Klainerman, Sergiu; Majda, Andrew 418 1981 The global nonlinear stability of the Minkowski space. Zbl 0827.53055Christodoulou, Demetrios; Klainerman, Sergiu 261 1993 Uniform decay estimates and the Lorentz invariance of the classical wave equation. Zbl 0635.35059Klainerman, Sergiu 236 1985 Compressible and incompressible fluids. Zbl 0478.76091Klainerman, Sergiu; Majda, Andrew 219 1982 Space-time estimates for null forms and the local existence theorem. Zbl 0803.35095Klainerman, S.; Machedon, M. 168 1993 Global existence for nonlinear wave equations. Zbl 0405.35056Klainerman, Sergiu 160 1980 The null condition and global existence to nonlinear wave equations. Zbl 0599.35105Klainerman, S. 146 1986 Global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions. Zbl 0597.35100Klainerman, Sergiu 134 1985 Global, small amplitude solutions to nonlinear evolution equations. Zbl 0509.35009Klainerman, S.; Ponce, Gustavo 126 1983 Almost global existence to nonlinear wave equations in three space dimensions. Zbl 0599.35104John, Fritz; Klainerman, S. 96 1984 Formation of singularities for wave equations including the nonlinear vibrating string. Zbl 0443.35040Klainerman, Sergiu; Majda, Andrew 85 1980 On almost global existence for nonrelativistic wave equations in 3D. Zbl 0867.35064Klainerman, Sergiu; Sideris, Thomas C. 80 1996 Long-time behavior of solutions to nonlinear evolution equations. Zbl 0502.35015Klainerman, Sergiu 79 1982 On the Maxwell-Klein-Gordon equation with finite energy. Zbl 0818.35123Klainerman, S.; Machedon, M. 77 1994 Smoothing estimates for null forms and applications. Zbl 0909.35094Klainerman, S.; Machedon, M. 72 1995 On the uniqueness of solutions to the Gross-Pitaevskii hierarchy. Zbl 1147.37034Klainerman, Sergiu; Machedon, Matei 70 2008 Remarks on the global Sobolev inequalities in the Minkowski space \({\mathbb{R}}^{n+1}\). Zbl 0686.46019Klainerman, S. 65 1987 The global nonlinear stability of the Minkowski space. Zbl 0733.35105Christodoulou, D.; Klainerman, S. 62 1990 Decay and regularity for the Schrödinger equation. Zbl 0802.35057Ben-Artzi, Matania; Klainerman, Sergiu 62 1992 Finite energy solutions of the Yang-Mills equations in \(\mathbb{R}^{3+1}\). Zbl 0827.53056Klainerman, S.; Machedon, M. 61 1995 Bilinear estimates and applications to nonlinear wave equations. Zbl 1146.35389Klainerman, Sergiu; Selberg, Sigmund 61 2002 The bounded \(L^2\) curvature conjecture. Zbl 1330.53089Klainerman, Sergiu; Rodnianski, Igor; Szeftel, Jeremie 55 2015 The evolution problem in general relativity. Zbl 1010.83004Klainerman, S.; Nicolò, Francesco 55 2003 On the optimal local regularity for the Yang-Mills equations in \(\mathbb{R}^{4+1}\). Zbl 0924.58010Klainerman, Sergiu; Tataru, Daniel 51 1999 Bilinear space-time estimates for homogeneous wave equations. Zbl 0959.35107Foschi, Damiano; Klainerman, Sergiu 43 2000 Remark on the optimal regularity for equations of wave maps type. Zbl 0884.35102Klainerman, Sergiu; Selberg, Sigmund 39 1997 Asymptotic properties of linear field equations in Minkowski space. Zbl 0715.35076Christodoulou, D.; Klainerman, S. 38 1990 A geometric approach to the Littlewood-Paley theory. Zbl 1206.35080Klainerman, S.; Rodnianski, I. 36 2006 A new approach to study the Vlasov-Maxwell system. Zbl 1037.35088Klainerman, Sergiu; Staffilani, Gigliola 35 2002 On the uniqueness of smooth, stationary black holes in vacuum. Zbl 1182.83005Ionescu, Alexandru D.; Klainerman, Sergiu 34 2009 Rough solutions of the Einstein-vacuum equations. Zbl 1089.83006Klainerman, Sergiu; Rodnianski, Igor 33 2005 Remark on Strichartz-type inequalities. (Appendices by Jean Bourgain and Daniel Tataru). Zbl 0853.35062Klainerman, Sergiu; Machedon, Matei 33 1996 On the formation of trapped surfaces. Zbl 1246.83028Klainerman, Sergiu; Rodnianski, Igor 32 2012 Causal geometry of Einstein-vacuum spacetimes with finite curvature flux. Zbl 1136.58018Klainerman, Sergiu; Rodnianski, Igor 32 2005 Improved local well-posedness for quasilinear wave equations in dimension three. Zbl 1031.35091Klainerman, S.; Rodnianski, I. 30 2003 On the global regularity of wave maps in the critical Sobolev norm. Zbl 0985.58009Klainerman, Sergiu; Rodnianski, Igor 29 2001 Uniqueness of smooth stationary black holes in vacuum: Small perturbations of the Kerr spaces. Zbl 1200.83059Alexakis, S.; Ionescu, A. D.; Klainerman, S. 28 2010 Peeling properties of asymptotically flat solutions to the Einstein vacuum equations. Zbl 1045.83016Klainerman, Sergiu; Nicolò, Francesco 26 2003 Small-data shock formation in solutions to 3D quasilinear wave equations: an overview. Zbl 1346.35005Holzegel, Gustav; Klainerman, Sergiu; Speck, Jared; Wong, Willie Wai-Yeung 25 2016 On the regularity properties of a model problem related to wave maps. Zbl 0878.35075Klainerman, Sergiu; Machedon, Matei 24 1997 A commuting vectorfields approach to Strichartz-type inequalities and applications to quasi-linear wave equations. Zbl 0993.35022Klainerman, S. 21 2001 On the breakdown criterion in general relativity. Zbl 1203.35084Klainerman, Sergiu; Rodnianski, Igor 21 2010 Global nonlinear stability of Schwarzschild spacetime under polarized perturbations. Zbl 1469.83002Klainerman, Sergiu; Szeftel, Jérémie 20 2020 On local and global aspects of the Cauchy problem in general relativity. Zbl 0944.83001Klainerman, Sergiu; Nicolò, Francesco 20 1999 Sharp trace theorems for null hypersurfaces on Einstein metrics with finite curvature flux. Zbl 1206.35081Klainerman, S.; Rodnianski, I. 20 2006 Hawking’s local rigidity theorem without analyticity. Zbl 1200.35302Alexakis, Spyros; Ionescu, Alexandru D.; Klainerman, Sergiu 20 2010 On ”almost global” solutions to quasilinear wave equations in three space dimensions. Zbl 0522.35063Klainerman, S. 19 1983 Remark on the asymptotic behavior of the Klein-Gordon equation in \(\mathbb{R}^{n+1}\). Zbl 0805.35104Klainerman, S. 18 1993 On the radius of injectivity of null hypersurfaces. Zbl 1198.53057Klainerman, Sergiu; Rodnianski, Igor 18 2008 Estimates for null forms and the spaces \(\mathbb{H}_{s,\delta}\). Zbl 0909.35095Klainerman, Sergiu; Machedon, Matei 17 1996 Weighted \(L^{\infty}\) and \(L^ 1\) estimates for solutions to the classical wave equation in three space dimensions. Zbl 0583.35068Klainerman, Sergiu 17 1984 A fully anisotropic mechanism for formation of trapped surfaces in vacuum. Zbl 1311.35311Klainerman, Sergiu; Luk, Jonathan; Rodnianski, Igor 16 2014 Uniqueness results for ill-posed characteristic problems in curved space-times. Zbl 1179.35338Ionescu, Alexandru D.; Klainerman, Sergiu 16 2009 On the optimal local regularity for gauge field theories. Zbl 0940.35011Klainerman, Sergiu; Machedon, Matei 16 1997 Smoothing estimates for null forms and applications. Zbl 0832.35096Klainerman, S.; Machedon, M. 15 1994 The causal structure of microlocalized rough Einstein metrics. Zbl 1089.83007Klainerman, Sergiu; Rodnianski, Igor 13 2005 A Kirchhoff-Sobolev parametrix for the wave equation and applications. Zbl 1148.35042Klainerman, Sergiu; Rodnianski, Igor 13 2007 Long time behaviour of solutions to nonlinear wave equations. Zbl 0581.35052Klainerman, Sergiu 12 1984 Global solution for massive Maxwell-Klein-Gordon equations. Zbl 1433.35386Klainerman, Sergiu; Wang, Qian; Yang, Shiwu 11 2020 Ricci defects of microlocalized Einstein metrics. Zbl 1063.53051Klainerman, Sergiu; Rodnianski, Igor 10 2004 On the local extension of Killing vector-fields in Ricci flat manifolds. Zbl 1276.53023Ionescu, Alexandru D.; Klainerman, Sergiu 10 2013 On the global stability of the wave-map equation in Kerr spaces with small angular momentum. Zbl 1396.83006Ionescu, Alexandru D.; Klainerman, Sergiu 9 2015 PDE as a unified subject. Special volume of the journal Geometric and Functional Analysis. Zbl 1002.35002Klainerman, Sergiu 9 2000 On emerging scarred surfaces for the Einstein vacuum equations. Zbl 1193.35225Klainerman, Sergiu; Rodnianski, Igor 9 2010 On the algebraic properties of the \(H_{n/2,1/2}\) spaces. Zbl 0919.46023Klainerman, Sergiu; Machedon, Matei 8 1998 Rigidity of stationary black holes with small angular momentum on the horizon. Zbl 1311.35309Alexakis, S.; Ionescu, A. D.; Klainerman, S. 8 2014 On the work and legacy of Fritz John, 1934-1991. Zbl 0929.01041Klainerman, S. 7 1998 A physical space approach to wave equation bilinear estimates. Zbl 1028.35111Klainerman, Sergiu; Rodnianski, Igor; Tao, Terence 7 2002 On the regularity properties of the wave equation. Zbl 0833.35093Klainerman, S.; Machedon, M. 6 1994 Rigidity results in general relativity: a review. Zbl 1339.83010Ionescu, Alexandru D.; Klainerman, Sergiu 6 2015 Rough solutions of the Einstein vacuum equations. Zbl 1008.35079Klainerman, Sergiu; Rodnianski, Igor 6 2002 Bilinear estimates on curved space-times. Zbl 1284.58018Klainerman, Sergiu; Rodnianski, Igor 6 2005 On Nash’s unique contribution to analysis in just three of his papers. Zbl 1364.35007Klainerman, Sergiu 5 2017 Explicit solutions of box u=0 on the Friedmann-Robertson-Walker space- times. Zbl 0499.58028Klainerman, S.; Sarnak, P. 5 1981 Global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions. Zbl 0627.35082Klainerman, S. 4 1987 On the regularity of classical field theories in Minkowski space-time \(\mathbb{R}^{3+1}\). Zbl 0909.53051Klainerman, S. 3 1997 Long time behaviour of solutions to nonlinear wave equations. Zbl 0578.35059Klainerman, S. 3 1985 Mathematical challenges of general relativity. Zbl 1215.35157Klainerman, Sergiu 3 2007 The nonlinear stability of the Minkowski metric in general relativity. Zbl 0695.53061Christodoulou, D.; Klainerman, S. 2 1989 Sharp \(L^1\) estimates for singular transport equations. Zbl 1144.35358Klainerman, Sergiu; Rodnianski, Igor 2 2008 Linear stability of black holes (following M. Dafermos and I. Rodnianski). Zbl 1361.53002Klainerman, Sergiu 1 2011 Einstein geometry and hyperbolic equations. Zbl 0648.53047Klainerman, S. 1 1988 The resolution of the bounded \(L^2\) curvature conjecture in general relativity. Zbl 1373.83018Klainerman, Sergiu; Rodnianski, Igor; Szeftel, Jérémie 1 2014 On the bounded \(L^2\)-curvature conjecture. Zbl 1304.53072Klainerman, Sergiu 1 2014 Corrigendum: Peeling properties of asymptotically flat solutions to the Einstein vacuum equations. Zbl 1057.83512Klainerman, S.; Nicolò, F. 1 2004 Mathematical challenges of general relativity. Zbl 1032.83001Klainerman, Sergiu 1 2002 Recent results in mathematical GR. Zbl 1267.83012Klainerman, Sergiu 1 2013 Fourier analysis and nonlinear wave equations. Zbl 0902.35074Klainerman, Sergiu 1 1998 Construction of GCM spheres in perturbations of Kerr. Zbl 07600219Klainerman, Sergiu; Szeftel, Jérémie 1 2022 Effective results on uniformization and intrinsic GCM spheres in perturbations of Kerr. Zbl 07600220Klainerman, Sergiu; Szeftel, Jérémie 1 2022 Construction of GCM spheres in perturbations of Kerr. Zbl 07600219Klainerman, Sergiu; Szeftel, Jérémie 1 2022 Effective results on uniformization and intrinsic GCM spheres in perturbations of Kerr. Zbl 07600220Klainerman, Sergiu; Szeftel, Jérémie 1 2022 Global nonlinear stability of Schwarzschild spacetime under polarized perturbations. Zbl 1469.83002Klainerman, Sergiu; Szeftel, Jérémie 20 2020 Global solution for massive Maxwell-Klein-Gordon equations. Zbl 1433.35386Klainerman, Sergiu; Wang, Qian; Yang, Shiwu 11 2020 On Nash’s unique contribution to analysis in just three of his papers. Zbl 1364.35007Klainerman, Sergiu 5 2017 Small-data shock formation in solutions to 3D quasilinear wave equations: an overview. Zbl 1346.35005Holzegel, Gustav; Klainerman, Sergiu; Speck, Jared; Wong, Willie Wai-Yeung 25 2016 The bounded \(L^2\) curvature conjecture. Zbl 1330.53089Klainerman, Sergiu; Rodnianski, Igor; Szeftel, Jeremie 55 2015 On the global stability of the wave-map equation in Kerr spaces with small angular momentum. Zbl 1396.83006Ionescu, Alexandru D.; Klainerman, Sergiu 9 2015 Rigidity results in general relativity: a review. Zbl 1339.83010Ionescu, Alexandru D.; Klainerman, Sergiu 6 2015 A fully anisotropic mechanism for formation of trapped surfaces in vacuum. Zbl 1311.35311Klainerman, Sergiu; Luk, Jonathan; Rodnianski, Igor 16 2014 Rigidity of stationary black holes with small angular momentum on the horizon. Zbl 1311.35309Alexakis, S.; Ionescu, A. D.; Klainerman, S. 8 2014 The resolution of the bounded \(L^2\) curvature conjecture in general relativity. Zbl 1373.83018Klainerman, Sergiu; Rodnianski, Igor; Szeftel, Jérémie 1 2014 On the bounded \(L^2\)-curvature conjecture. Zbl 1304.53072Klainerman, Sergiu 1 2014 On the local extension of Killing vector-fields in Ricci flat manifolds. Zbl 1276.53023Ionescu, Alexandru D.; Klainerman, Sergiu 10 2013 Recent results in mathematical GR. Zbl 1267.83012Klainerman, Sergiu 1 2013 On the formation of trapped surfaces. Zbl 1246.83028Klainerman, Sergiu; Rodnianski, Igor 32 2012 Linear stability of black holes (following M. Dafermos and I. Rodnianski). Zbl 1361.53002Klainerman, Sergiu 1 2011 Uniqueness of smooth stationary black holes in vacuum: Small perturbations of the Kerr spaces. Zbl 1200.83059Alexakis, S.; Ionescu, A. D.; Klainerman, S. 28 2010 On the breakdown criterion in general relativity. Zbl 1203.35084Klainerman, Sergiu; Rodnianski, Igor 21 2010 Hawking’s local rigidity theorem without analyticity. Zbl 1200.35302Alexakis, Spyros; Ionescu, Alexandru D.; Klainerman, Sergiu 20 2010 On emerging scarred surfaces for the Einstein vacuum equations. Zbl 1193.35225Klainerman, Sergiu; Rodnianski, Igor 9 2010 On the uniqueness of smooth, stationary black holes in vacuum. Zbl 1182.83005Ionescu, Alexandru D.; Klainerman, Sergiu 34 2009 Uniqueness results for ill-posed characteristic problems in curved space-times. Zbl 1179.35338Ionescu, Alexandru D.; Klainerman, Sergiu 16 2009 On the uniqueness of solutions to the Gross-Pitaevskii hierarchy. Zbl 1147.37034Klainerman, Sergiu; Machedon, Matei 70 2008 On the radius of injectivity of null hypersurfaces. Zbl 1198.53057Klainerman, Sergiu; Rodnianski, Igor 18 2008 Sharp \(L^1\) estimates for singular transport equations. Zbl 1144.35358Klainerman, Sergiu; Rodnianski, Igor 2 2008 A Kirchhoff-Sobolev parametrix for the wave equation and applications. Zbl 1148.35042Klainerman, Sergiu; Rodnianski, Igor 13 2007 Mathematical challenges of general relativity. Zbl 1215.35157Klainerman, Sergiu 3 2007 A geometric approach to the Littlewood-Paley theory. Zbl 1206.35080Klainerman, S.; Rodnianski, I. 36 2006 Sharp trace theorems for null hypersurfaces on Einstein metrics with finite curvature flux. Zbl 1206.35081Klainerman, S.; Rodnianski, I. 20 2006 Rough solutions of the Einstein-vacuum equations. Zbl 1089.83006Klainerman, Sergiu; Rodnianski, Igor 33 2005 Causal geometry of Einstein-vacuum spacetimes with finite curvature flux. Zbl 1136.58018Klainerman, Sergiu; Rodnianski, Igor 32 2005 The causal structure of microlocalized rough Einstein metrics. Zbl 1089.83007Klainerman, Sergiu; Rodnianski, Igor 13 2005 Bilinear estimates on curved space-times. Zbl 1284.58018Klainerman, Sergiu; Rodnianski, Igor 6 2005 Ricci defects of microlocalized Einstein metrics. Zbl 1063.53051Klainerman, Sergiu; Rodnianski, Igor 10 2004 Corrigendum: Peeling properties of asymptotically flat solutions to the Einstein vacuum equations. Zbl 1057.83512Klainerman, S.; Nicolò, F. 1 2004 The evolution problem in general relativity. Zbl 1010.83004Klainerman, S.; Nicolò, Francesco 55 2003 Improved local well-posedness for quasilinear wave equations in dimension three. Zbl 1031.35091Klainerman, S.; Rodnianski, I. 30 2003 Peeling properties of asymptotically flat solutions to the Einstein vacuum equations. Zbl 1045.83016Klainerman, Sergiu; Nicolò, Francesco 26 2003 Bilinear estimates and applications to nonlinear wave equations. Zbl 1146.35389Klainerman, Sergiu; Selberg, Sigmund 61 2002 A new approach to study the Vlasov-Maxwell system. Zbl 1037.35088Klainerman, Sergiu; Staffilani, Gigliola 35 2002 A physical space approach to wave equation bilinear estimates. Zbl 1028.35111Klainerman, Sergiu; Rodnianski, Igor; Tao, Terence 7 2002 Rough solutions of the Einstein vacuum equations. Zbl 1008.35079Klainerman, Sergiu; Rodnianski, Igor 6 2002 Mathematical challenges of general relativity. Zbl 1032.83001Klainerman, Sergiu 1 2002 On the global regularity of wave maps in the critical Sobolev norm. Zbl 0985.58009Klainerman, Sergiu; Rodnianski, Igor 29 2001 A commuting vectorfields approach to Strichartz-type inequalities and applications to quasi-linear wave equations. Zbl 0993.35022Klainerman, S. 21 2001 Bilinear space-time estimates for homogeneous wave equations. Zbl 0959.35107Foschi, Damiano; Klainerman, Sergiu 43 2000 PDE as a unified subject. Special volume of the journal Geometric and Functional Analysis. Zbl 1002.35002Klainerman, Sergiu 9 2000 On the optimal local regularity for the Yang-Mills equations in \(\mathbb{R}^{4+1}\). Zbl 0924.58010Klainerman, Sergiu; Tataru, Daniel 51 1999 On local and global aspects of the Cauchy problem in general relativity. Zbl 0944.83001Klainerman, Sergiu; Nicolò, Francesco 20 1999 On the algebraic properties of the \(H_{n/2,1/2}\) spaces. Zbl 0919.46023Klainerman, Sergiu; Machedon, Matei 8 1998 On the work and legacy of Fritz John, 1934-1991. Zbl 0929.01041Klainerman, S. 7 1998 Fourier analysis and nonlinear wave equations. Zbl 0902.35074Klainerman, Sergiu 1 1998 Remark on the optimal regularity for equations of wave maps type. Zbl 0884.35102Klainerman, Sergiu; Selberg, Sigmund 39 1997 On the regularity properties of a model problem related to wave maps. Zbl 0878.35075Klainerman, Sergiu; Machedon, Matei 24 1997 On the optimal local regularity for gauge field theories. Zbl 0940.35011Klainerman, Sergiu; Machedon, Matei 16 1997 On the regularity of classical field theories in Minkowski space-time \(\mathbb{R}^{3+1}\). Zbl 0909.53051Klainerman, S. 3 1997 On almost global existence for nonrelativistic wave equations in 3D. Zbl 0867.35064Klainerman, Sergiu; Sideris, Thomas C. 80 1996 Remark on Strichartz-type inequalities. (Appendices by Jean Bourgain and Daniel Tataru). Zbl 0853.35062Klainerman, Sergiu; Machedon, Matei 33 1996 Estimates for null forms and the spaces \(\mathbb{H}_{s,\delta}\). Zbl 0909.35095Klainerman, Sergiu; Machedon, Matei 17 1996 Smoothing estimates for null forms and applications. Zbl 0909.35094Klainerman, S.; Machedon, M. 72 1995 Finite energy solutions of the Yang-Mills equations in \(\mathbb{R}^{3+1}\). Zbl 0827.53056Klainerman, S.; Machedon, M. 61 1995 On the Maxwell-Klein-Gordon equation with finite energy. Zbl 0818.35123Klainerman, S.; Machedon, M. 77 1994 Smoothing estimates for null forms and applications. Zbl 0832.35096Klainerman, S.; Machedon, M. 15 1994 On the regularity properties of the wave equation. Zbl 0833.35093Klainerman, S.; Machedon, M. 6 1994 The global nonlinear stability of the Minkowski space. Zbl 0827.53055Christodoulou, Demetrios; Klainerman, Sergiu 261 1993 Space-time estimates for null forms and the local existence theorem. Zbl 0803.35095Klainerman, S.; Machedon, M. 168 1993 Remark on the asymptotic behavior of the Klein-Gordon equation in \(\mathbb{R}^{n+1}\). Zbl 0805.35104Klainerman, S. 18 1993 Decay and regularity for the Schrödinger equation. Zbl 0802.35057Ben-Artzi, Matania; Klainerman, Sergiu 62 1992 The global nonlinear stability of the Minkowski space. Zbl 0733.35105Christodoulou, D.; Klainerman, S. 62 1990 Asymptotic properties of linear field equations in Minkowski space. Zbl 0715.35076Christodoulou, D.; Klainerman, S. 38 1990 The nonlinear stability of the Minkowski metric in general relativity. Zbl 0695.53061Christodoulou, D.; Klainerman, S. 2 1989 Einstein geometry and hyperbolic equations. Zbl 0648.53047Klainerman, S. 1 1988 Remarks on the global Sobolev inequalities in the Minkowski space \({\mathbb{R}}^{n+1}\). Zbl 0686.46019Klainerman, S. 65 1987 Global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions. Zbl 0627.35082Klainerman, S. 4 1987 The null condition and global existence to nonlinear wave equations. Zbl 0599.35105Klainerman, S. 146 1986 Uniform decay estimates and the Lorentz invariance of the classical wave equation. Zbl 0635.35059Klainerman, Sergiu 236 1985 Global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions. Zbl 0597.35100Klainerman, Sergiu 134 1985 Long time behaviour of solutions to nonlinear wave equations. Zbl 0578.35059Klainerman, S. 3 1985 Almost global existence to nonlinear wave equations in three space dimensions. Zbl 0599.35104John, Fritz; Klainerman, S. 96 1984 Weighted \(L^{\infty}\) and \(L^ 1\) estimates for solutions to the classical wave equation in three space dimensions. Zbl 0583.35068Klainerman, Sergiu 17 1984 Long time behaviour of solutions to nonlinear wave equations. Zbl 0581.35052Klainerman, Sergiu 12 1984 Global, small amplitude solutions to nonlinear evolution equations. Zbl 0509.35009Klainerman, S.; Ponce, Gustavo 126 1983 On ”almost global” solutions to quasilinear wave equations in three space dimensions. Zbl 0522.35063Klainerman, S. 19 1983 Compressible and incompressible fluids. Zbl 0478.76091Klainerman, Sergiu; Majda, Andrew 219 1982 Long-time behavior of solutions to nonlinear evolution equations. Zbl 0502.35015Klainerman, Sergiu 79 1982 Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. Zbl 0476.76068Klainerman, Sergiu; Majda, Andrew 418 1981 Explicit solutions of box u=0 on the Friedmann-Robertson-Walker space- times. Zbl 0499.58028Klainerman, S.; Sarnak, P. 5 1981 Global existence for nonlinear wave equations. Zbl 0405.35056Klainerman, Sergiu 160 1980 Formation of singularities for wave equations including the nonlinear vibrating string. Zbl 0443.35040Klainerman, Sergiu; Majda, Andrew 85 1980 all cited Publications top 5 cited Publications all top 5 Cited by 1,795 Authors 35 Klainerman, Sergiu 29 Hayashi, Nakao 29 Rodnianski, Igor 29 Wang, Shu 22 Feireisl, Eduard 22 Ionescu, Alexandru D. 22 Tataru, Daniel 22 Zhou, Yi 21 Naumkin, Pavel Ivanovich 19 Speck, Jared 19 Zha, Dongbing 18 Lindblad, Hans 17 Katayama, Soichiro 16 Pecher, Hartmut 16 Schochet, Steven H. 16 Yang, Jianwei 15 Hidano, Kunio 15 Ju, Qiangchang 15 Peng, Yuejun 15 Tao, Terence 15 Wang, Chengbo 15 Yin, Huicheng 14 Li, Fucai 14 Luk, Jonathan 14 Metcalfe, Jason L. 14 Novotný, Antonín 14 Oh, Sung-Jin 14 Pavlović, Nataša 14 Ponce, Gustavo 14 Sogge, Christopher D. 14 Wei, Changhua 13 Chen, Thomas 13 Feng, Yuehong 13 Jiang, Song 13 Kenig, Carlos Eduardo 13 Machedon, Matei 13 Ou, Yaobin 13 Selberg, Sigmund 12 Kong, Dexing 11 Chruściel, Piotr Tadeusz 11 Georgiev, Vladimir S. 11 Krieger, Joachim 11 Li, Xin 11 Lusanna, Luca 11 Masmoudi, Nader 11 Smulevici, Jacques 11 Sugimoto, Mitsuru 11 Tsutsumi, Yoshio 10 Chen, Xuwen 10 Donninger, Roland 10 Grillakis, Manoussos G. 10 Guo, Zihua 10 Lei, Zhen 10 Ozawa, Tohru 10 Sunagawa, Hideaki 10 Valiente Kroon, Juan Antonio 10 Wang, Qian 10 Yang, Shiwu 9 Baldi, Pietro 9 Beirão da Veiga, Hugo 9 Dafermos, Mihalis 9 D’Ancona, Piero 9 Delort, Jean-Marc 9 Dong, Shijie 9 Fang, Daoyuan 9 Godin, Paul 9 Guo, Boling 9 Huh, Hyungjin 9 Kwon, Young-Sam 9 LeFloch, Philippe Gerard 9 Schütz, Jochen 9 Shao, Arick 9 Soffer, Avraham 9 Staffilani, Gigliola 9 Sterbenz, Jacob 9 Vega, Luis 9 Yu, Pin 8 Alinhac, Serge 8 Bournaveas, Nikolaos 8 Burq, Nicolas 8 Disconzi, Marcelo Mendes 8 Dumbser, Michael 8 Komech, Alexander Ilich 8 Rendall, Alan D. 8 Sideris, Thomas C. 8 Tesfahun, Achenef 8 Witt, Ingo 8 Wong, Willie Wai-Yeung 7 Aretakis, Stefanos 7 Ben-Artzi, Matania 7 Berti, Massimiliano 7 Candy, Timothy 7 Foschi, Damiano 7 Herr, Sebastian 7 Holzegel, Gustav 7 Joudioux, Jérémie 7 Klein, Rupert 7 Munz, Claus-Dieter 7 Nakanishi, Kenji 7 Paetz, Tim-Torben ...and 1,695 more Authors all top 5 Cited in 263 Serials 132 Communications in Mathematical Physics 119 Journal of Differential Equations 111 Communications in Partial Differential Equations 71 Archive for Rational Mechanics and Analysis 66 Journal of Hyperbolic Differential Equations 55 Journal of Functional Analysis 54 Journal of Mathematical Physics 53 Journal of Mathematical Analysis and Applications 49 Annales Henri Poincaré 49 Annals of PDE 47 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 35 Discrete and Continuous Dynamical Systems 32 Journal of Computational Physics 32 Journal of High Energy Physics 30 Nonlinear Analysis. Theory, Methods & Applications 28 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 28 Journal de Mathématiques Pures et Appliquées. Neuvième Série 28 SIAM Journal on Mathematical Analysis 27 Transactions of the American Mathematical Society 27 Communications on Pure and Applied Analysis 26 General Relativity and Gravitation 26 ZAMP. Zeitschrift für angewandte Mathematik und Physik 26 Inventiones Mathematicae 25 Classical and Quantum Gravity 25 Advances in Mathematics 24 Duke Mathematical Journal 20 Mathematical Methods in the Applied Sciences 20 Mathematische Zeitschrift 18 Bulletin of the American Mathematical Society. New Series 17 Journal of the American Mathematical Society 16 Calculus of Variations and Partial Differential Equations 16 Analysis & PDE 15 Journal d’Analyse Mathématique 15 Mathematische Annalen 14 Computers and Fluids 14 Proceedings of the American Mathematical Society 14 NoDEA. Nonlinear Differential Equations and Applications 14 Journal of Mathematical Fluid Mechanics 14 Living Reviews in Relativity 13 Communications in Contemporary Mathematics 13 Nonlinear Analysis. Real World Applications 13 Comptes Rendus. Mathématique. Académie des Sciences, Paris 12 Communications on Pure and Applied Mathematics 12 Journal of Geometry and Physics 12 Applied Mathematics and Computation 12 Journal of the European Mathematical Society (JEMS) 11 Annals of Mathematics. Second Series 11 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 Nonlinearity 10 Annales de l’Institut Fourier 10 Quarterly of Applied Mathematics 10 Journal of Nonlinear Science 10 Journal of Evolution Equations 9 Chinese Annals of Mathematics. Series B 9 Acta Applicandae Mathematicae 9 Physica D 9 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 9 Science China. Mathematics 9 Séminaire Laurent Schwartz. EDP et Applications 8 Applicable Analysis 8 Annali di Matematica Pura ed Applicata. Serie Quarta 8 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 8 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 7 Letters in Mathematical Physics 7 Reviews in Mathematical Physics 7 Memoirs of the American Mathematical Society 7 Proceedings of the Japan Academy. Series A 7 Publications of the Research Institute for Mathematical Sciences, Kyoto University 7 Applied Numerical Mathematics 7 Journal of Scientific Computing 7 Journal of Dynamics and Differential Equations 7 Acta Mathematica Sinica. English Series 7 Boundary Value Problems 6 Computer Methods in Applied Mechanics and Engineering 6 Revista Matemática Iberoamericana 6 Annales de l’Institut Henri Poincaré. Physique Théorique 6 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 6 Selecta Mathematica. New Series 6 Kinetic and Related Models 5 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 5 Journal of the Mathematical Society of Japan 5 Osaka Journal of Mathematics 5 SIAM Journal on Numerical Analysis 5 SIAM Journal on Scientific Computing 5 The Journal of Fourier Analysis and Applications 5 International Journal of Geometric Methods in Modern Physics 5 Communications in Computational Physics 4 Computers & Mathematics with Applications 4 Journal of Fluid Mechanics 4 Physics of Fluids, A 4 Arkiv för Matematik 4 Acta Mathematica 4 Manuscripta Mathematica 4 Asymptotic Analysis 4 Forum Mathematicum 4 Physical Review Letters 4 Differential Equations 4 Acta Mathematica Scientia. Series B. (English Edition) 4 SN Partial Differential Equations and Applications 3 Journal of Statistical Physics ...and 163 more Serials all top 5 Cited in 50 Fields 1,746 Partial differential equations (35-XX) 516 Fluid mechanics (76-XX) 413 Relativity and gravitational theory (83-XX) 215 Quantum theory (81-XX) 208 Differential geometry (53-XX) 142 Global analysis, analysis on manifolds (58-XX) 89 Numerical analysis (65-XX) 89 Statistical mechanics, structure of matter (82-XX) 79 Dynamical systems and ergodic theory (37-XX) 62 Mechanics of deformable solids (74-XX) 54 Optics, electromagnetic theory (78-XX) 53 Harmonic analysis on Euclidean spaces (42-XX) 40 Mechanics of particles and systems (70-XX) 38 Operator theory (47-XX) 34 Functional analysis (46-XX) 28 Geophysics (86-XX) 22 Calculus of variations and optimal control; optimization (49-XX) 15 Ordinary differential equations (34-XX) 14 Classical thermodynamics, heat transfer (80-XX) 14 Astronomy and astrophysics (85-XX) 12 History and biography (01-XX) 11 Probability theory and stochastic processes (60-XX) 9 Integral equations (45-XX) 7 General and overarching topics; collections (00-XX) 7 Systems theory; control (93-XX) 6 Algebraic geometry (14-XX) 6 Topological groups, Lie groups (22-XX) 5 Real functions (26-XX) 5 Measure and integration (28-XX) 5 Approximations and expansions (41-XX) 5 Abstract harmonic analysis (43-XX) 4 Special functions (33-XX) 3 Functions of a complex variable (30-XX) 3 Difference and functional equations (39-XX) 3 Geometry (51-XX) 3 General topology (54-XX) 3 Manifolds and cell complexes (57-XX) 3 Computer science (68-XX) 3 Biology and other natural sciences (92-XX) 2 Number theory (11-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Integral transforms, operational calculus (44-XX) 2 Information and communication theory, circuits (94-XX) 1 Mathematical logic and foundations (03-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Statistics (62-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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