Topic · Navier-Stokes equation solutions
Most cited papers in Navier-Stokes equation solutions
What are the most cited papers in Navier-Stokes equation solutions?
The most cited paper in Navier-Stokes equation solutions is "Numerical solution of the Navier-Stokes equations" (ALEXANDRE JOEL CHORIN, 1968), with 5,401 citations. Next come "The numerical simulation of two-dimensional fluid flow with strong shocks" (2,944) and "Systems of conservation laws" (2,682).
Showing 50 of 98 papers. Every paper with more than 443 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | Numerical solution of the Navier-Stokes equations ALEXANDRE JOEL CHORIN · Mathematics of Computation | 1968 | 5,401 |
| 2 | The numerical simulation of two-dimensional fluid flow with strong shocks Paul R. Woodward, Phillip Colella · Journal of Computational Physics | Apr 1984 | 2,944 |
| 3 | Systems of conservation laws Peter D. Lax, Burton Wendroff · Communications on Pure and Applied Mathematics | May 1960 | 2,682 |
| 4 | A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws Gary A. Sod · Journal of Computational Physics | Apr 1978 | 2,678 |
| 5 | Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works Jay P. Boris, David Book · Journal of Computational Physics | 1973 | 2,131 |
| 6 | Commutator estimates and the euler and navier‐stokes equations Tosio Kato, Gustavo Henrique Santos Flores Ponce · Communications on Pure and Applied Mathematics | Oct 1988 | 1,919 |
| 7 | Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations Jean Bourgain · Geometric and Functional Analysis | May 1993 | 1,697 |
| 8 | A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem Jean‐David Benamou, Yann Brenier · Numerische Mathematik | 2000 | 1,694 |
| 9 | Flux-vector splitting for the Euler equations Bram van Leer · Lecture notes in physics | 1982 | 1,635 |
| 10 | Remarks on the breakdown of smooth solutions for the 3-D Euler equations J. Thomas Beale, T. Kato, Andrew J. Majda · Communications in Mathematical Physics | Mar 1984 | 1,592 |
| 11 | On the stability of heterogeneous shear flows John W. Miles · Journal of Fluid Mechanics | Jun 1961 | 1,527 |
| 12 | Universality and scaling in gravitational collapse of a massless scalar field Matthew W. Choptuik · Physical Review Letters | 4 Jan 1993 | 1,458 |
| 13 | Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle Carlos E. Kenig, Gustavo Henrique Santos Flores Ponce, Luis Vega · Communications on Pure and Applied Mathematics | Apr 1993 | 1,417 |
| 14 | Numerical study of slightly viscous flow ALEXANDRE JOEL CHORIN · Journal of Fluid Mechanics | 6 Mar 1973 | 1,414 |
| 15 | On the nature of turbulence David Pierre Ruelle, Floris Takens · Communications in Mathematical Physics | Dec 1971 | 1,393 |
| 16 | StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions Tosio Kato · Mathematische Zeitschrift | Dec 1984 | 1,348 |
| 17 | On the Navier-Stokes initial value problem. I Hiroshi Fujita, Tosio Kato · Archive for Rational Mechanics and Analysis | 1964 | 1,334 |
| 18 | Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation Élliott H. Lieb · Studies in Applied Mathematics | Oct 1977 | 1,306 |
| 19 | Upwind methods for hyperbolic conservation laws with source terms Alfredo Bermúdez, Ma Elena Vazquez · Computers & Fluids | Nov 1994 | 1,052 |
| 20 | On the interior regularity of weak solutions of the Navier-Stokes equations James B Serrin · Archive for Rational Mechanics and Analysis | 1962 | 1,044 |
| 21 | Uniformly High-Order Accurate Nonoscillatory Schemes. I Ami Harten, Stanley Osher · SIAM Journal on Numerical Analysis | Apr 1987 | 1,016 |
| 22 | Convergence to Steady State Solutions of the Euler Equations on Unstructured Grids with Limiters Venkat N. Venkatakrishnan · Journal of Computational Physics | Apr 1995 | 987 |
| 23 | Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation Luis A. Caffarelli, Alexis Vasseur · Annals of Mathematics | 25 Apr 2010 | 946 |
| 24 | Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids Sergiù Klainerman, Andrew J. Majda · Communications on Pure and Applied Mathematics | Jul 1981 | 940 |
| 25 | On Some Questions in Boundary Value Problems of Mathematical Physics J. L. Lions · North-Holland mathematics studies | 1978 | 939 |
| 26 | Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system Yoshikazu Giga · Journal of Differential Equations | Apr 1986 | 910 |
| 27 | The relaxation schemes for systems of conservation laws in arbitrary space dimensions Shi Jin, Zhouping Xin · Communications on Pure and Applied Mathematics | 1995 | 909 |
| 28 | Well-posedness for the Navier–Stokes Equations Herbert Koch, Daniel Tataru · Advances in Mathematics | 2001 | 892 |
| 29 | On the Existence of Globally Defined Weak Solutions to the Navier—Stokes Equations Eduard Feireisl, Antonín Novotný, Hana Petzeltová · Journal of Mathematical Fluid Mechanics | Nov 2001 | 874 |
| 30 | Saddle points and instability of nonlinear hyperbolic equations Lawrence Edward Payne, David H. Sattinger · Israel Journal of Mathematics | Dec 1975 | 845 |
| 31 | Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids Akitaka Matsumura, Takaaki Nishida · Communications in Mathematical Physics | Dec 1983 | 832 |
| 32 | Nonlinear scalar field equations, II existence of infinitely many solutions Henri Berestycki, Pierre‐Louis Lions · Archive for Rational Mechanics and Analysis | Dec 1983 | 806 |
| 33 | Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar Peter Constantin, Andrew J. Majda, Esteban G. Tabak · Nonlinearity | Nov 1994 | 722 |
| 34 | On optimum design in fluid mechanics Olivier Pironneau · Journal of Fluid Mechanics | 3 Jun 1974 | 690 |
| 35 | Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation Adrian Constantin, Joachim Escher · Communications on Pure and Applied Mathematics | May 1998 | 684 |
| 36 | Hyperbolic conservation laws with stiff relaxation terms and entropy Gui‐Qiang Chen, C. David Levermore, Tai‐Ping Liu · Communications on Pure and Applied Mathematics | Jun 1994 | 676 |
| 37 | Immiscible cellular-automaton fluids Daniel H. Rothman, Jeffrey M. Keller · Journal of Statistical Physics | Aug 1988 | 660 |
| 38 | Gevrey class regularity for the solutions of the Navier-Stokes equations Ciprian Foiaş, Roger Témam · Journal of Functional Analysis | Dec 1989 | 656 |
| 39 | Physical acceptability of isolated, static, spherically symmetric, perfect fluid solutions of Einstein's equations M.S.R. Delgaty, Kayll Lake · Computer Physics Communications | Dec 1998 | 650 |
| 40 | Regularity Results for Stationary Electro-Rheological Fluids E. Acerbi, Giuseppe Mingione · Archive for Rational Mechanics and Analysis | Sep 2002 | 647 |
| 41 | A Maximum Principle Applied to Quasi-Geostrophic Equations Antonio Córdoba, Diego Córdoba · Communications in Mathematical Physics | 16 Mar 2004 | 647 |
| 42 | Martingale and stationary solutions for stochastic Navier-Stokes equations Franco Flandoli, Dariusz Gątarek · Probability Theory and Related Fields | Sep 1995 | 642 |
| 43 | Transport equation and Cauchy problem for BV vector fields Luigi Ambrosio · Inventiones mathematicae | Apr 2004 | 641 |
| 44 | Hyperbolic systems of conservation laws Peter D. Lax · Courant lecture notes in mathematics | 12 Dec 2006 | 634 |
| 45 | Systems of Conservation Equations with a Convex Extension Kurt O. Friedrichs, Peter D. Lax · Proceedings of the National Academy of Sciences | Aug 1971 | 633 |
| 46 | Optimal Control with State-Space Constraint I Halil Mete Soner · SIAM Journal on Control and Optimization | May 1986 | 619 |
| 47 | Nonparabolic dissipative systems modeling the flow of liquid crystals Fang‐Hua Lin, Chun Liu · Communications on Pure and Applied Mathematics | 1995 | 616 |
| 48 | Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data K. Pfaffelmoser · Journal of Differential Equations | Feb 1992 | 610 |
| 49 | Nonstationary flows of viscous and ideal fluids in R3 Tosio Kato · Journal of Functional Analysis | Mar 1972 | 604 |
| 50 | A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description Emanuele Caglioti, Pierre Louis Lions, Carlo Marchioro et al. · Communications in Mathematical Physics | 1992 | 600 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.