Edit Profile (opens in new tab) DiPerna, Ronald J. Compute Distance To: Compute Author ID: diperna.ronald-j Published as: DiPerna, Ronald J.; DiPerna, R. J.; Di Perna, Ronald J.; Diperna, Ronald J.; DiPerna, Ronald; Di Perna, Ronald; Di Perna, R.-J.; Diperna, R. J. External Links: MGP · Wikidata Documents Indexed: 50 Publications since 1973 Co-Authors: 4 Co-Authors with 16 Joint Publications 297 Co-Co-Authors Co-Authors 34 single-authored 11 Lions, Pierre-Louis 4 Majda, Andrew J. 1 Dafermos, Constantine M. 1 Meyer, Yves F. all top 5 Serials 6 Archive for Rational Mechanics and Analysis 4 Communications in Mathematical Physics 4 Communications on Pure and Applied Mathematics 2 Indiana University Mathematics Journal 2 Journal of Differential Equations 2 Comptes Rendus de l’Académie des Sciences. Série I 1 Inventiones Mathematicae 1 Transactions of the American Mathematical Society 1 Rendiconti del Seminario Matematico 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Physica D 1 Journal of the American Mathematical Society 1 Annals of Mathematics. Second Series all top 5 Fields 43 Partial differential equations (35-XX) 19 Fluid mechanics (76-XX) 5 Numerical analysis (65-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Functional analysis (46-XX) 2 Ordinary differential equations (34-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Integral equations (45-XX) 2 Mechanics of deformable solids (74-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 General topology (54-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 36 Publications have been cited 3,048 times in 2,426 Documents Cited by ▼ Year ▼ Ordinary differential equations, transport theory and Sobolev spaces. Zbl 0696.34049DiPerna, R. J.; Lions, P. L. 799 1989 On the Cauchy problem for Boltzmann equations: Global existence and weak stability. Zbl 0698.45010DiPerna, R. J.; Lions, P. L. 498 1989 Convergence of approximate solutions to conservation laws. Zbl 0519.35054DiPerna, R. J. 233 1983 Measure-valued solutions to conservation laws. Zbl 0616.35055Diperna, Ronald J. 202 1985 Oscillations and concentrations in weak solutions of the incompressible fluid equations. Zbl 0626.35059DiPerna, Ronald J.; Majda, Andrew J. 184 1987 Convergence of the viscosity method for isentropic gas dynamics. Zbl 0533.76071DiPerna, Ronald J. 183 1983 Global weak solutions of Vlasov-Maxwell systems. Zbl 0698.35128DiPerna, R. J.; Lions, P. L. 160 1989 Uniqueness of solutions to hyperbolic conservation laws. Zbl 0409.35057Diperna, Ronald J. 111 1979 Concentrations in regularizations for \(2-D\) incompressible flow. Zbl 0850.76730Diperna, Ronald J.; Majda, Andrew J. 107 1987 \(L^ p\) regularity of velocity averages. Zbl 0763.35014DiPerna, R. J.; Lions, P. L.; Meyer, Y. 81 1991 On the Fokker-Planck-Boltzmann equation. Zbl 0671.35068DiPerna, R. J.; Lions, P. L. 64 1988 Compensated compactness and general systems of conservation laws. Zbl 0606.35052Di Perna, Ronald J. 45 1985 Reduced Hausdorff dimension and concentration-cancellation for two- dimensional incompressible flow. Zbl 0707.76026DiPerna, Ronald J.; Majda, Andrew 43 1988 Global solutions of Boltzmann’s equation and the entropy inequality. Zbl 0724.45011DiPerna, R. J.; Lions, P. L. 40 1991 Solutions globals d’équations du type Vlasov-Poisson. (Global solutions of Vlasov-Poisson type equations). Zbl 0682.35022DiPerna, Ronald; Lions, Pierre-Louis 39 1988 Global existence of solutions to nonlinear hyperbolic systems of conservation laws. Zbl 0314.58010DiPerna, Ronald J. 32 1976 Global solutions to a class of nonlinear hyperbolic systems of equations. Zbl 0256.35053Diperna, Ronald J. 31 1973 The Riemann problem for certain classes of hyperbolic systems of conservation laws. Zbl 0323.35050Dafermos, C. M.; DiPerna, R. J. 30 1976 The validity of nonlinear geometric optics for weak solutions of conservation laws. Zbl 0582.35081Di Perna, Ronald J.; Majda, Andrew 26 1985 Singularities of solutions of nonlinear hyperbolic systems of conservation laws. Zbl 0324.35062DiPerna, Ronald J. 26 1975 Decay and asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws. Zbl 0309.35050DiPerna, Ronald J. 24 1975 Existence in the large for quasilinear hyperbolic conservation laws. Zbl 0268.35066DiPerna, Ronald J. 21 1973 Global weak solutions of kinetic equations. Zbl 0813.35087DiPerna, R. J.; Lions, Pierre-Louis 19 1988 Équations différentielles ordinaires et équations de transport avec des coefficients irréguliers. (Errata ci-joint). (Ordinary differential equations and transport equations with irregular coefficients. (Errata enclosed)). Zbl 0708.34014DiPerna, R. J.; Lions, P. L. 11 1989 Decay of solutions of hyperbolic systems of conservation laws with a convex extension. Zbl 0348.35071DiPerna, Ronald J. 11 1977 Solutions globales de l’équation de Boltzmann. (Global solutions of the Boltzmann equation). Zbl 0662.35016Di Perna, Ronald; Lions, Pierre-Louis 10 1988 The structure of solutions to hyperbolic conservation laws. Zbl 0434.35061DiPerna, R. J. 4 1979 Degenerate systems of conservation laws. Zbl 0595.35076Diperna, R. J. 3 1985 Solutions globales de l’équation de Boltzmann. (Global solutions of the Boltzmann equation). Zbl 0666.35059Di Perna, R.-J.; Lions, P.-L. 2 1988 Convergence of approximate solutions to conservation laws. Zbl 0491.76011DiPerna, R. J. 2 1982 Conservation laws and compensated compactness. Zbl 0555.35087DiPerna, Ronald J. 2 1984 Global solutions to a class of nonlinear hyperbolic systems of equations. Zbl 0243.35068DiPerna, Ronald 1 1973 Singularities and oscillations in solutions to conservation laws. Zbl 0585.35064DiPerna, Ronald J. 1 1984 Finite difference schemes for conservation laws. Zbl 0494.65054DiPerna, Ronald J. 1 1982 Generalized solutions to conservation laws. Zbl 0542.35048DiPerna, Ronald J. 1 1983 Entropy and the uniqueness of solutions to hyperbolic conservation laws. Zbl 0469.35064DiPerna, R. J. 1 1978 \(L^ p\) regularity of velocity averages. Zbl 0763.35014DiPerna, R. J.; Lions, P. L.; Meyer, Y. 81 1991 Global solutions of Boltzmann’s equation and the entropy inequality. Zbl 0724.45011DiPerna, R. J.; Lions, P. L. 40 1991 Ordinary differential equations, transport theory and Sobolev spaces. Zbl 0696.34049DiPerna, R. J.; Lions, P. L. 799 1989 On the Cauchy problem for Boltzmann equations: Global existence and weak stability. Zbl 0698.45010DiPerna, R. J.; Lions, P. L. 498 1989 Global weak solutions of Vlasov-Maxwell systems. Zbl 0698.35128DiPerna, R. J.; Lions, P. L. 160 1989 Équations différentielles ordinaires et équations de transport avec des coefficients irréguliers. (Errata ci-joint). (Ordinary differential equations and transport equations with irregular coefficients. (Errata enclosed)). Zbl 0708.34014DiPerna, R. J.; Lions, P. L. 11 1989 On the Fokker-Planck-Boltzmann equation. Zbl 0671.35068DiPerna, R. J.; Lions, P. L. 64 1988 Reduced Hausdorff dimension and concentration-cancellation for two- dimensional incompressible flow. Zbl 0707.76026DiPerna, Ronald J.; Majda, Andrew 43 1988 Solutions globals d’équations du type Vlasov-Poisson. (Global solutions of Vlasov-Poisson type equations). Zbl 0682.35022DiPerna, Ronald; Lions, Pierre-Louis 39 1988 Global weak solutions of kinetic equations. Zbl 0813.35087DiPerna, R. J.; Lions, Pierre-Louis 19 1988 Solutions globales de l’équation de Boltzmann. (Global solutions of the Boltzmann equation). Zbl 0662.35016Di Perna, Ronald; Lions, Pierre-Louis 10 1988 Solutions globales de l’équation de Boltzmann. (Global solutions of the Boltzmann equation). Zbl 0666.35059Di Perna, R.-J.; Lions, P.-L. 2 1988 Oscillations and concentrations in weak solutions of the incompressible fluid equations. Zbl 0626.35059DiPerna, Ronald J.; Majda, Andrew J. 184 1987 Concentrations in regularizations for \(2-D\) incompressible flow. Zbl 0850.76730Diperna, Ronald J.; Majda, Andrew J. 107 1987 Measure-valued solutions to conservation laws. Zbl 0616.35055Diperna, Ronald J. 202 1985 Compensated compactness and general systems of conservation laws. Zbl 0606.35052Di Perna, Ronald J. 45 1985 The validity of nonlinear geometric optics for weak solutions of conservation laws. Zbl 0582.35081Di Perna, Ronald J.; Majda, Andrew 26 1985 Degenerate systems of conservation laws. Zbl 0595.35076Diperna, R. J. 3 1985 Conservation laws and compensated compactness. Zbl 0555.35087DiPerna, Ronald J. 2 1984 Singularities and oscillations in solutions to conservation laws. Zbl 0585.35064DiPerna, Ronald J. 1 1984 Convergence of approximate solutions to conservation laws. Zbl 0519.35054DiPerna, R. J. 233 1983 Convergence of the viscosity method for isentropic gas dynamics. Zbl 0533.76071DiPerna, Ronald J. 183 1983 Generalized solutions to conservation laws. Zbl 0542.35048DiPerna, Ronald J. 1 1983 Convergence of approximate solutions to conservation laws. Zbl 0491.76011DiPerna, R. J. 2 1982 Finite difference schemes for conservation laws. Zbl 0494.65054DiPerna, Ronald J. 1 1982 Uniqueness of solutions to hyperbolic conservation laws. Zbl 0409.35057Diperna, Ronald J. 111 1979 The structure of solutions to hyperbolic conservation laws. Zbl 0434.35061DiPerna, R. J. 4 1979 Entropy and the uniqueness of solutions to hyperbolic conservation laws. Zbl 0469.35064DiPerna, R. J. 1 1978 Decay of solutions of hyperbolic systems of conservation laws with a convex extension. Zbl 0348.35071DiPerna, Ronald J. 11 1977 Global existence of solutions to nonlinear hyperbolic systems of conservation laws. Zbl 0314.58010DiPerna, Ronald J. 32 1976 The Riemann problem for certain classes of hyperbolic systems of conservation laws. Zbl 0323.35050Dafermos, C. M.; DiPerna, R. J. 30 1976 Singularities of solutions of nonlinear hyperbolic systems of conservation laws. Zbl 0324.35062DiPerna, Ronald J. 26 1975 Decay and asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws. Zbl 0309.35050DiPerna, Ronald J. 24 1975 Global solutions to a class of nonlinear hyperbolic systems of equations. Zbl 0256.35053Diperna, Ronald J. 31 1973 Existence in the large for quasilinear hyperbolic conservation laws. Zbl 0268.35066DiPerna, Ronald J. 21 1973 Global solutions to a class of nonlinear hyperbolic systems of equations. Zbl 0243.35068DiPerna, Ronald 1 1973 all cited Publications top 5 cited Publications all top 5 Cited by 1,989 Authors 63 Feireisl, Eduard 37 Chen, Gui-Qiang G. 33 Yang, Tong 31 Crippa, Gianluca 25 Novotný, Antonín 25 Perthame, Benoît 24 Vasseur, Alexis F. 22 Frid, Hermano 22 Zhang, Xianwen 21 Gwiazda, Piotr 21 Huang, Feimin 21 Lu, Yunguang 20 Jabin, Pierre-Emmanuel 20 Nečasová, Šárka 19 LeFloch, Philippe Gerard 18 Masmoudi, Nader 18 Panov, Evgeniy Yu. 18 Redwane, Hicham 17 Ambrosio, Luigi 17 Wang, Dehua 17 Zhang, Ping 16 Cercignani, Carlo 16 Desvillettes, Laurent 16 Flandoli, Franco 16 Lions, Pierre-Louis 16 Luo, Dejun 16 Tadmor, Eitan 15 Bouchut, François 15 Saint-Raymond, Laure 15 Xin, Zhouping 15 Zhao, Huijiang 14 Nussenzveig Lopes, Helena Judith 14 Serre, Denis 14 Zhu, Changjiang 13 DiPerna, Ronald J. 13 Marcati, Pierangelo 13 Tzavaras, Athanasios E. 12 Bostan, Mihai 12 De Lellis, Camillo 12 Duan, Renjun 12 Karlsen, Kenneth Hvistendahl 12 Kreml, Ondřej 12 Kružík, Martin 12 Lopes Filho, Milton da Costa 12 Mishra, Siddhartha 12 Zvyagin, Viktor Grigor’evich 11 Golse, François 11 Goudon, Thierry 11 Liu, Tai-Ping 11 Mischler, Stéphane 11 Świerczewska-Gwiazda, Agnieszka 11 Trivisa, Konstantina 11 Wittbold, Petra 10 Arkeryd, Leif O. 10 Bennouna, Jaouad 10 Brenier, Yann 10 Dafermos, Constantine M. 10 Hofmanová, Martina 10 Majda, Andrew J. 10 Orlov, Vladimir P. 10 Petzeltová, Hana 10 Röckner, Michael 10 Slemrod, Marshall 10 Ukai, Seiji 10 Wiedemann, Emil 9 Alexandre, Radjesvarane 9 Blanchard, Dominique 9 Bressan, Alberto 9 Ducomet, Bernard 9 Guibé, Olivier 9 Ha, Seung-Yeal 9 Han-Kwan, Daniel 9 Kwon, Young-Sam 9 Shaposhnikov, Stanislav V. 9 Spirito, Stefano 9 Székelyhidi, László jun. 9 Winkler, Michael 8 Bardos, Claude Williams 8 Bianchini, Stefano 8 Bogachev, Vladimir Igorevich 8 Carrillo de la Plata, José Antonio 8 Donatelli, Donatella 8 Ghoshal, Shyam Sundar 8 Giesselmann, Jan 8 Guo, Yan 8 Hauray, Maxime 8 Jiang, Ning 8 Kang, Moon-Jin 8 Mitrovic, Darko 8 Neves, Wladimir 8 Olivera, Christian 8 Orenga, Pierre 8 Rindler, Filip 8 Seis, Christian 8 Skubachevskiĭ, Aleksandr Leonidovich 8 Strain, Robert M. 8 Tsuge, Naoki 8 Zheng, Yuxi 8 Zhou, Shulin 7 Alberti, Giovanni ...and 1,889 more Authors all top 5 Cited in 308 Serials 194 Archive for Rational Mechanics and Analysis 176 Journal of Differential Equations 93 Communications in Partial Differential Equations 82 Communications in Mathematical Physics 73 Journal of Mathematical Analysis and Applications 59 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 56 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 56 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 52 Journal de Mathématiques Pures et Appliquées. Neuvième Série 50 Journal of Hyperbolic Differential Equations 49 SIAM Journal on Mathematical Analysis 41 Journal of Statistical Physics 34 Journal of Functional Analysis 33 Journal of Mathematical Fluid Mechanics 33 Comptes Rendus. Mathématique. Académie des Sciences, Paris 32 Mathematics of Computation 29 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 29 Nonlinear Analysis. Real World Applications 28 Communications on Pure and Applied Mathematics 26 Physica D 25 Calculus of Variations and Partial Differential Equations 24 Quarterly of Applied Mathematics 24 Transactions of the American Mathematical Society 24 Nonlinear Analysis. Theory, Methods & Applications 23 Journal of Mathematical Physics 23 Journal of Mathematical Sciences (New York) 23 Kinetic and Related Models 20 Mathematical Methods in the Applied Sciences 18 Nonlinearity 18 ZAMP. Zeitschrift für angewandte Mathematik und Physik 17 NoDEA. Nonlinear Differential Equations and Applications 17 Journal of Evolution Equations 16 Applicable Analysis 16 Transport Theory and Statistical Physics 15 Annali di Matematica Pura ed Applicata. Serie Quarta 15 Discrete and Continuous Dynamical Systems 15 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 14 Journal of Computational Physics 14 Inventiones Mathematicae 14 Numerische Mathematik 14 Acta Applicandae Mathematicae 14 Applied Mathematics Letters 14 Séminaire Laurent Schwartz. EDP et Applications 13 Advances in Mathematics 12 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 12 Stochastic Processes and their Applications 12 Bulletin of the American Mathematical Society. New Series 12 Doklady Mathematics 12 Acta Mathematica Sinica. English Series 12 Science China. Mathematics 12 Annals of PDE 11 Proceedings of the American Mathematical Society 10 SIAM Journal on Numerical Analysis 10 Revista Matemática Iberoamericana 10 Journal of Nonlinear Science 10 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 10 Bulletin des Sciences Mathématiques 10 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 9 Acta Mathematicae Applicatae Sinica. English Series 9 Journal of the American Mathematical Society 8 Zeitschrift für Analysis und ihre Anwendungen 8 Journal of Dynamics and Differential Equations 7 Applied Mathematics and Optimization 7 Duke Mathematical Journal 7 Ricerche di Matematica 7 Studies in Applied Mathematics 7 RAIRO. Modélisation Mathématique et Analyse Numérique 7 Japan Journal of Industrial and Applied Mathematics 7 Applications of Mathematics 7 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 7 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 7 Analysis and Applications (Singapore) 7 Stochastic and Partial Differential Equations. Analysis and Computations 6 Computer Methods in Applied Mechanics and Engineering 6 The Annals of Probability 6 Manuscripta Mathematica 6 Mathematische Annalen 6 Chinese Annals of Mathematics. Series B 6 Journal of Scientific Computing 6 Potential Analysis 6 Networks and Heterogeneous Media 5 Journal of Fluid Mechanics 5 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 5 Monatshefte für Mathematik 5 Rendiconti del Seminario Matematico della Università di Padova 5 Siberian Mathematical Journal 5 Mathematical and Computer Modelling 5 Applicationes Mathematicae 5 Journal of the European Mathematical Society (JEMS) 5 Bulletin of the Brazilian Mathematical Society. New Series 5 Multiscale Modeling & Simulation 5 Mediterranean Journal of Mathematics 5 Boundary Value Problems 5 Proceedings of the Steklov Institute of Mathematics 5 Discrete and Continuous Dynamical Systems. Series S 5 Advances in Calculus of Variations 4 Mathematical Notes 4 Journal of Computational and Applied Mathematics 4 Probability Theory and Related Fields 4 Journal of Integral Equations and Applications ...and 208 more Serials all top 5 Cited in 46 Fields 2,036 Partial differential equations (35-XX) 1,008 Fluid mechanics (76-XX) 389 Statistical mechanics, structure of matter (82-XX) 219 Numerical analysis (65-XX) 160 Probability theory and stochastic processes (60-XX) 131 Calculus of variations and optimal control; optimization (49-XX) 108 Mechanics of deformable solids (74-XX) 95 Functional analysis (46-XX) 76 Biology and other natural sciences (92-XX) 66 Ordinary differential equations (34-XX) 60 Dynamical systems and ergodic theory (37-XX) 58 Integral equations (45-XX) 53 Optics, electromagnetic theory (78-XX) 51 Operator theory (47-XX) 43 Classical thermodynamics, heat transfer (80-XX) 38 Global analysis, analysis on manifolds (58-XX) 37 Measure and integration (28-XX) 31 Real functions (26-XX) 26 Relativity and gravitational theory (83-XX) 25 Systems theory; control (93-XX) 24 Harmonic analysis on Euclidean spaces (42-XX) 23 Quantum theory (81-XX) 23 Astronomy and astrophysics (85-XX) 22 Mechanics of particles and systems (70-XX) 22 Geophysics (86-XX) 21 Differential geometry (53-XX) 20 Operations research, mathematical programming (90-XX) 12 Functions of a complex variable (30-XX) 12 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 10 General topology (54-XX) 7 Computer science (68-XX) 5 Approximations and expansions (41-XX) 4 General and overarching topics; collections (00-XX) 4 History and biography (01-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Statistics (62-XX) 4 Information and communication theory, circuits (94-XX) 3 Special functions (33-XX) 3 Convex and discrete geometry (52-XX) 2 Integral transforms, operational calculus (44-XX) 2 Manifolds and cell complexes (57-XX) 1 Mathematical logic and foundations (03-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Topological groups, Lie groups (22-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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