# List of scientific equations named after people

This is a list of scientific equations named after people (eponymous equations).
* A
* B
* C
* D
* E
* F
* G
* H
* I
* J
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* L
* M
* N
* O
* P
* R
* S
* T
* V
* W
* Y
* Z
* See also
* References
| Equation | Field | Person(s) named after |
| Adams–Williamson equation | Seismology | L. H. Adams and E. D. Williamson |
| Allen–Cahn equation | Phase separation | S. Allen and John W. Cahn |
| Archard equation | Materials science | John F. Archard |
| Arrhenius equation | Chemical kinetics | Svante Arrhenius |
| Aryabhata equation | Number theory | Aryabhata |
| Ashkin–Teller model | Statistical mechanics | Edward Teller Julius Ashkin |
| Avrami equation | Phase transformation | Melvin Avrami |
| Batchelor–Chandrasekhar equation | Turbulence | George Batchelor and Subrahmanyan Chandrasekhar |
| Bateman equation | Radioactivity | Harry Bateman |
| Bellman equation | Control theory | Richard Bellman |
| Beltrami equation | Differential geometry | Eugenio Beltrami |
| Benedict–Webb–Rubin equation | Fluid dynamics | M. Benedict, G. B. Webb, and L. C. Rubin |
| Benjamin–Bona–Mahony equation Benjamin–Ono equation | Fluid dynamics, Wave mechanics Waves in fluids | T. B. Benjamin, J. L. Bona, and J. J. Mahony T. B. Benjamin and H. Ono |
| Bernoulli's equation | Fluid dynamics | Daniel Bernoulli |
| Bernoulli differential equation | Calculus | Jacob Bernoulli |
| Bessel differential equation | Special functions | Friedrich Bessel |
| Birch–Murnaghan equation of state | Continuum mechanics | Francis Birch and Francis D. Murnaghan |
| Birkhoff–Rott equation | Fluid dynamics | Garrett Birkhoff |
| Black's equation | Electronics | James R. Black |
| Black–Scholes equation | Mathematical finance | Fischer Black and Myron Scholes |
| Blaney–Criddle equation | Agronomy | Blaney and Criddle |
| Boltzmann equation | Thermodynamics | Ludwig Boltzmann |
| Bôcher's equation | Calculus | Maxime Bôcher |
| Borda–Carnot equation | Fluid dynamics | Jean-Charles de Borda and Lazare Carnot |
| Boussinesq equations | Wave mechanics | Joseph Boussinesq |
| Breit equation | Quantum mechanics | Gregory Breit |
| Bridgman's equation Bridgman's thermodynamic equations | Dimensional analysis Thermodynamics | Percy Williams Bridgman Percy Williams Bridgman |
| Broer–Kaup–Kupershmidt equation | Wave mechanics | Lambertus Broer, D. J. Kaup, and B. A. Kupershmidt |
| Buckley–Leverett equation | Two-phase flow in porous media | S. E. Buckley and M. C. Leverett |
| Burgers' equation | Fluid dynamics | Johannes Martinus Burgers |
| Cahn–Hilliard equation | Phase separation | John W. Cahn and John E. Hilliard |
| Callan–Symanzik equation | Quantum field theory | Curtis Callan and Kurt Symanzik |
| Callendar–Van Dusen equation | Thermodynamics | Hugh Longbourne Callendar and M. S. Van Dusen |
| Camassa–Holm equation | Fluid dynamics | Roberto Camassa and Darryl Holm |
| Carmona-Orbezo number | Flow electrode capacitive deionization | Aranzazu Carmona-Orbezo |
| Carothers equation | Polymer chemistry | Wallace Carothers |
| Cauchy's equation Cauchy momentum equation Cauchy's functional equation Cauchy's integral formula Cauchy–Euler equation Cauchy–Riemann equations | Optics Fluid dynamics Functional theory Complex analysis Calculus Complex analysis | Augustin Louis Cauchy Augustin Louis Cauchy Augustin Louis Cauchy Augustin Louis Cauchy Augustin Louis Cauchy and Leonhard Euler Augustin Louis Cauchy and Bernhard Riemann |
| Cesàro equation | Differential geometry | Ernesto Cesàro |
| Chandrasekhar–Page equations | General relativity | Subrahmanyan Chandrasekhar and Page |
| Chaplygin's equation | Transonic flow | Sergey Chaplygin |
| Chapman–Kolmogorov equation Chapman–Enskog equation | Probability theory Kinetic theory | Sydney Chapman and Andrey Kolmogorov Sydney Chapman and David Enskog |
| Chebyshev equation | Calculus | Pafnuty Chebyshev |
| Chrystal's equation | Differential equations | George Chrystal |
| Churchill–Bernstein equation | Heat Transfer | S. W. Churchill and M. Bernstein |
| Clairaut's equation | Calculus | Alexis Clairaut |
| Clarke's equation | Combustion | John Frederick Clarke |
| Clausius–Clapeyron equation | Calculus | Rudolf Clausius and Émile Clapeyron |
| Clausius–Mossotti equation | Physics | Rudolf Clausius and Ottaviano-Fabrizio Mossotti |
| Colebrook equation Colebrook–White equation | Fluid dynamics Fluid dynamics | C. F. Colebrook C. F. Colebrook and F. M. White |
| Competitive Lotka–Volterra equations | Population dynamics | Alfred J. Lotka and Vito Volterra |
| Conformal Killing equation | Topology, Differential geometry | Wilhelm Killing |
| Darcy–Weisbach equation | Fluid dynamics | Henry Darcy and Julius Weisbach |
| Davey–Stewartson equation | Fluid dynamics | A. Davey and K. Stewartson |
| Debye–Hückel equation | Electrochemistry | Peter Debye and Erich Hückel |
| Degasperis–Procesi equation | Mathematical physics | Antonio Degasperis and M. Procesi |
| Dehn–Sommerville equations | Geometry | Max Dehn and Duncan Sommerville |
| Diophantine equation | Mathematics | Diophantus of Alexandria |
| Dirac equation Dirac equation in APS | Quantum mechanics Quantum field theory | Paul Dirac Paul Dirac |
| Doppler equations | Wave mechanics | Christian Doppler |
| Drake equation | Cosmology | Frank Drake |
| Duffing equation | Differential equations | Duffing |
| Dym equation | Wave mechanics | Harry Dym |
| Einstein field equations | General relativity | Albert Einstein |
| Ernst equation | PDE | Frederick J. Ernst |
| Euler equations (fluid dynamics) Euler's equations (rigid body dynamics) Euler–Bernoulli beam equation Euler–Lagrange equation Euler–Darboux equation Euler–Poisson–Darboux equation Euler–Tricomi equation | Fluid dynamics Rigid body dynamics Solid mechanics Calculus of variations Calculus Calculus Calculus | Leonhard Euler Leonhard Euler Leonhard Euler and Daniel Bernoulli Leonhard Euler and Joseph Louis Lagrange Leonhard Euler and Jean Darboux Euler, Poisson, and Jean Darboux Leonhard Euler and Francesco Tricomi |
| Exner equation | Geology, Sedimentology | Felix Maria Exner |
| Eyring–Polanyi equation | Chemical kinetics | Henry Eyring and Michael Polanyi |
| Faddeev equations | Quantum mechanics | Ludvig Faddeev |
| Falkner–Skan equation | Boundary layer flow | V. M. Falkner and S. W. Skan |
| Falkowich–Kármán equation | Transonic flow | Falkowich and Theodore von Kármán |
| Fenske equation | Distillation | Merrell Fenske |
| Fisher equation | Financial mathematics | Irving Fisher |
| Fisher's equation | Mathematics | Ronald Fisher |
| Fokker–Planck equation | Probability theory | Adriaan Fokker and Max Planck |
| Föppl–von Kármán equations | Elasticity | August Föppl and Theodore von Kármán |
| Fowler–Nordheim equation | Condensed matter physics | Ralph H. Fowler and Lothar Wolfgang Nordheim |
| Fredholm integral equation | Integral equations | Erik Fredholm |
| Fresnel equations | Wave optics | Augustin-Jean Fresnel |
| Friedmann equations | Cosmology | Alexander Friedman |
| Gauss–Codazzi equations Gauss–Codazzi equations (relativity) | Riemannian geometry General relativity | Carl Friedrich Gauss and Delfino Codazzi Carl Friedrich Gauss and Delfino Codazzi |
| Gibbs–Duhem equation Gibbs–Helmholtz equation | Thermodynamics Thermodynamics | Josiah Willard Gibbs and Pierre Duhem Josiah Willard Gibbs and Hermann von Helmholtz |
| Ginzburg–Landau equation | Superconductivity | Lev Landau and Vitaly Ginzburg |
| Goldman–Hodgkin–Katz flux equation Goldman–Hodgkin–Katz voltage equation | Electrochemistry Electrochemistry | David E. Goldman, Alan Hodgkin, and Bernard Katz David E. Goldman, Alan Hodgkin, and Bernard Katz |
| Grad–Shafranov equation | Magnetohydrodynamics, Plasma physics | H. Grad and Vitaly D. Shafranov |
| Green–Kubo relations | Statistical mechanics | M. S. Green and Ryogo Kubo |
| Gross–Pitaevskii equation | Condensed matter physics | E. P. Gross and Lev P. Pitaevskii |
| Haaland equation | Fluid dynamics | S. E. Haaland |
| Hadamard–Rybczynski equation | Bubble dynamics | Jacques Hadamard and Witold Rybczyński |
| Hamilton–Jacobi equation Hamilton–Jacobi–Bellman equation | Hamiltonian mechanics Optimal control | William Hamilton and Carl Gustav Jacobi William Hamilton, Carl Gustav Jacobi, and Richard Bellman |
| Hammett equation | Organic chemistry | Louis Plack Hammett |
| Hankinson's equation | Wood science | Hankinson |
| Hartree equation | Atomic physics | Douglas Hartree |
| Hartree–Fock equation | Quantum chemistry | Douglas Hartree and Vladimir Fock |
| Hasegawa–Mima equation | Plasma physics | Akira Hasegawa and Kunioki Mima |
| Hazen–Williams equation | Hydraulics, Irrigation | Hazen and Williams |
| Helmholtz equation | Electromagnetic radiation, Seismology, Acoustics | Hermann von Helmholtz |
| Henderson–Hasselbalch equation | Chemistry | Lawrence Joseph Henderson and Karl Albert Hasselbalch |
| Heun's equation | Calculus | Karl L. W. M. Heun |
| Hicks equation | Fluid dynamics | William Mitchinson Hicks |
| Hill equation (biochemistry) | Biochemistry | Archibald Vivian Hill |
| Hill differential equation | Orbital mechanics | George William Hill |
| Hugoniot equation | Compressible flows | Pierre Henri Hugoniot |
| Hunter–Saxton equation Hunter–Zheng equation | Liquid crystals PDE | John K. Hunter and Ralph Saxton John K. Hunter and Yuxi Zheng |
| Ishimori equation | PDE | Y. Ishimori |
| John's equation | Calculus | Fritz John |
| Johnson–Holmquist equation of state | Ceramic science | Johnson Holmquist |
| Kadomtsev–Petviashvili equation Kadomtsev–Petviashvili–Burgers equation | Wave mechanics Wave mechanics | B. B. Kadomtsev and V. I. Petviashvili B. B. Kadomtsev, V. I. Petviashvili, and J. M. Burgers |
| Kapustinskii equation | Crystallography | Anatoli Kapustinskii |
| Kármán–Howarth equation | Turbulence | Theodore von Kármán and Leslie Howarth |
| Karplus equation | Nuclear magnetic resonance | Martin Karplus |
| Kaup–Kupershmidt equation | Wave mechanics | D. J. Kaup and B. A. Kupershmidt |
| Kepler's equation | Astronomy | Johannes Kepler |
| Klein–Gordon equation | Quantum field theory | Oskar Klein and Walter Gordon |
| Kohn–Sham equations | Mathematics | Walter Kohn and Lu Jeu Sham |
| Kolmogorov backward equation | Probability distribution | Andrey Kolmogorov |
| Kolmogorov–Feller equation | Probabilistic models | Andrey Kolmogorov and William Feller |
| Korteweg–de Vries equation | Wave mechanics, Solitons | Diederik Korteweg and Gustav de Vries |
| Kozeny–Carman equation | Fluid dynamics, Unit operations | Josef Kozeny and Philip C. Carman |
| Krichever–Novikov equation | Lie algebra | I. M. Krichever and Sergei Novikov |
| Laguerre's equation | Differential equation | Edmond Laguerre |
| Lamm equation | Sedimentation theory | O. Lamm |
| Landau–Lifshitz equation | Aeroacoustics | Lev Landau and Evgeny Lifshitz |
| Landau–Lifshitz–Gilbert equation | Magnetization | Lev Landau, Evgeny Lifshitz, and T. L. Gilbert |
| Lane–Emden equation | Astrophysics | Jonathan Homer Lane and Robert Emden |
| Langevin equation | Statistical physics | Paul Langevin |
| Laplace's equation Laplace's tidal equations | Electromagnetism, Fluid dynamics Fluid dynamics | Pierre-Simon Laplace Pierre-Simon Laplace |
| Legendre's equation | Spherical harmonics | Adrien-Marie Legendre |
| Leonard–Merritt formula | Astrophysics | Peter Leonard and David Merritt |
| Levy–Mises equations | Solid mechanics | Paul Lévy and Richard von Mises |
| Liénard equation | Dynamical systems | Alfred-Marie Liénard |
| Lighthill equation | Aeroacoustics | James Lighthill |
| Lindblad equation | Quantum mechanics | G. Lindblad |
| Lin–Tsien equation | PDE | Lin and Tsien |
| Liñán's equation | Combustion | Amable Liñán |
| Lindley equation | Queueing theory | Dennis Lindley |
| Liouville equations | Differential geometry | Joseph Liouville |
| Lommel differential equation | Calculus | Eugen von Lommel |
| Lorentz equation | Electromagnetism | Hendrik Lorentz |
| Lorentz–Lorenz equation | Optics | Hendrik Lorentz and Ludvig Lorenz |
| Lotka–Volterra equation | Biological systems | Alfred J. Lotka and Vito Volterra |
| Lyapunov equation | Control theory | Aleksandr Lyapunov |
| Madelung equations | Quantum mechanics | Erwin Madelung |
| Majorana equation | Quantum field theory | Ettore Majorana |
| Manakov equation | Wave mechanics, Fiber optics | S. V. Manakov |
| Marchenko equation | Scattering theory | Vladimir Marchenko |
| Mark–Houwink equation | Polymer chemistry | Herman Francis Mark and Houwink |
| Mason equation | Atmospheric thermodynamics | Basil John Mason |
| Mason–Weaver equation | Sedimentation theory | Max Mason and Warren Weaver |
| Mathieu equation | Periodic phenomena, Parametric resonance | Émile Léonard Mathieu |
| Mathisson–Papapetrou–Dixon equations | General relativity, Gravitational waves | Mathisson, A. Papapetrou, and G. W. Dixon |
| Maurer–Cartan equation | Lie groups, Differential geometry | Ludwig Maurer and Élie Joseph Cartan |
| Maxwell's equations Maxwell relations | Electrodynamics Thermodynamics | James Clerk Maxwell James Clerk Maxwell |
| Mayo–Lewis equation | Polymer chemistry | Frank R. Mayo and Frederick M. Lewis |
| Michaelis–Menten equation | Chemical kinetics | Leonor Michaelis and Maud Menten |
| Monge–Ampère equation | Calculus | Gaspard Monge and André-Marie Ampère |
| Morison equation | Fluid dynamics | J. R. Morison |
| Nahm equations | Differential equations | Werner Nahm |
| Navier–Stokes equations | Fluid dynamics | Claude-Louis Navier and George Gabriel Stokes |
| Nernst equation | Electrochemistry | Walther Nernst |
| Neugebauer equations | Printing systems | Hans E. J. Neugebauer |
| Newton–Euler equations | Classical mechanics | Isaac Newton and Leonhard Euler |
| Nonlinear Schrödinger equation | Theoretical physics | Erwin Schrödinger |
| Ornstein–Zernike equation | Statistical mechanics | Leonard Ornstein and Frits Zernike |
| Painlevé equations | Differential equations | Paul Painlevé |
| Orr–Sommerfeld equation | Fluid dynamics, Stability analysis | William McFadden Orr and Arnold Sommerfeld |
| Osipkov–Merritt model | Astrophysics | Leonid Osipkov and David Merritt |
| Papapetrou–Dixon equations | General relativity, Gravitational waves | A. Papapetrou and G. W. Dixon |
| Pauli equation | Quantum mechanics | Wolfgang Pauli |
| Pell's equation | Number theory | John Pell |
| Penman equation Penman–Monteith equation | Agronomy Agronomy | Howard Penman Howard Penman and J. L. Monteith |
| Picard–Fuchs equation | Calculus | Charles Émile Picard and Lazarus Fuchs |
| Poisson's equation Poisson–de Rham equation | Calculus Astrophysics | Siméon Denis Poisson Siméon Denis Poisson and Georges de Rham |
| Pople—Nesbet equations | Quantum Chemistry | John Pople and R. K. Nesbet |
| Prandtl–Glauert equation | Compressible flows | Ludwig Prandtl and Hermann Glauert |
| Price equation | Evolutionary dynamics, Evolutionary biology | George R. Price |
| Prony equation | Hydraulics | Gaspard de Prony |
| Rabinovich–Fabrikant equations | Chaotic systems | M. I. Rabinovich and A. L. Fabrikant |
| Ramanujan–Nagell equation | Number theory | Srinivasa Ramanujan and Trygve Nagell |
| Randles–Sevcik equation | Cyclic voltammetry | John Edward Brough Randles |
| Rankine–Hugoniot equation | Compressible flows | William Rankine and Pierre Henri Hugoniot |
| Rarita–Schwinger equation | Quantum electrodynamics | William Rarita and Julian Schwinger |
| Raychaudhuri equation | General relativity | Amal Kumar Raychaudhuri |
| Rayleigh's equation Rayleigh–Pitot equation Rayleigh–Plesset equation | Stability of inviscid flows Gas dynamics Bubble oscillation | Lord Rayleigh Lord Rayleigh and Henri Pitot Lord Rayleigh and Milton S. Plesset |
| Reynolds-averaged Navier–Stokes equations | Turbulent flows | Osborne Reynolds, Claude-Louis Navier, and George Stokes |
| Relativistic Euler equations | Astrophysics, Fluid dynamics | Leonhard Euler |
| Riccati equation | Calculus | Jacopo Riccati |
| Richards equation | Hydrology | Lorenzo Richards |
| Riemann theta function Riemann zeta function Riemann's differential equation | Special functions Number theory Differential equation | Bernhard Riemann Bernhard Riemann Bernhard Riemann |
| Rodrigues equation | Chromatography | Alirio E. Rodrigues |
| Roothaan equations or Roothaan–Hall equations | Quantum chemistry | Clemens Roothaan and George Hall |
| Sackur–Tetrode equation | Statistical thermodynamics | Hugo Martin Tetrode and Otto Sackur |
| Sagan equation | Cosmology | Carl Sagan |
| Saha–Langmuir equation | Quantum mechanics, Statistical mechanics | Megh Nad Saha and Irving Langmuir |
| Saint-Venant equations | Fluid dynamics | Adhémar Jean Claude Barré de Saint-Venant |
| Sakuma–Hattori equation | Thermal radiation | Fumihiro Sakuma and Susumu Hattori |
| Sawada–Kotera equation | Wave mechanics | K. Sawada and T. Kotera |
| Scheil–Gulliver equation | Metallurgy | G. H. Gulliver and E. Scheil |
| Schrödinger equation Schrödinger–Newton equations | Quantum mechanics Quantum mechanics | Erwin Schrödinger Erwin Schrödinger and Isaac Newton |
| Schwinger–Dyson equation | Quantum field theory | Julian Schwinger and Freeman Dyson |
| Screened Poisson equation | Plasma physics | Siméon Denis Poisson |
| Seiberg–Witten equation | PDE | Nathan Seiberg and Edward Witten |
| Sellmeier equation | Optics | W. Sellmeier |
| sine–Gordon equation | Solitons | Walter Gordon |
| Slutsky equation | Consumer theory | Eugen Slutsky |
| Souders–Brown equation | Separation processes | M. Souders and G. G. Brown |
| Starling equation | Fluid dynamics | Ernest Starling |
| Stokes–Einstein equation | Diffusion of particles | George Gabriel Stokes and Albert Einstein |
| Strominger's equations | Heterotic string theory | Andrew Strominger |
| Stuart–Landau equation | Fluid dynamics | John Trevor Stuart and Lev Landau |
| Sturm–Liouville equation | Differential equation | Jacques Charles François Sturm and Joseph Liouville |
| Swamee–Jain equation | Fluid dynamics | P. K. Swamee and A. K. Jain |
| Swift–Hohenberg equation | Pattern formation | J. B. Swift and P. C. Hohenberg |
| Sylvester equation Sylvester's formula | Control theory Matrix theory | James Sylvester James Sylvester |
| Taft equation | Physical organic chemistry | Robert W. Taft |
| Tanaka equation | Stochastic theory | Hiroshi Tanaka |
| Taylor–Goldstein equation | Fluid dynamics | G.I. Taylor and Sydney Goldstein |
| Torricelli's equation | Mechanics | Evangelista Torricelli |
| Tricomi equation | Partial differential equations | Francesco Tricomi |
| Tsiolkovsky rocket equation | Astrodynamics | Konstantin Tsiolkovsky |
| Van Deemter's equation | Chromatography | J. J. Van Deemter |
| Van der Pol equation | Dynamical systems | Balthasar van der Pol |
| Van der Waals equation | Thermodynamics | Johannes Diderik van der Waals |
| Van 't Hoff equation | Chemical thermodynamics | Jacobus Henricus van 't Hoff |
| Verhulst equation | Population dynamics | Pierre François Verhulst |
| Vlasov equation Vlasov–Poisson equation | Plasma physics Plasma physics | Anatoly Vlasov Anatoly Vlasov and Siméon Denis Poisson |
| Volterra integral equation | Integral equations | Vito Volterra |
| Wald's equation | Probability theory | Abraham Wald |
| Washburn's equation | Flow in porous media | Edward W. Washburn |
| Weber's equation | Differential equation | Heinrich Friedrich Weber |
| Welch–Satterthwaite equation | Statistics, Uncertainty analysis | B. L. Welch and F. E. Satterthwaite |
| Wheeler–deWitt equation | Quantum gravity | John Archibald Wheeler and Bryce DeWitt |
| Whewell equation | Geometry | William Whewell |
| Whitham equation | Wave mechanics, Solitons | Gerald Whitham |
| Wiener equation | Brownian motion | Norbert Wiener |
| Yang–Baxter equation Yang–Mills–Higgs equations | Statistical mechanics Gauge theory, Quantum field theory | Chen Ning Yang and Rodney J. Baxter Chen Ning Yang, Robert Mills, and Peter Higgs |
| Young–Dupré equation Young–Laplace equation | Interfacial dynamics Fluid dynamics | Thomas Young and Lewis Dupré Thomas Young and Pierre-Simon Laplace |
| Zakai equation | Stochastic differential equations | M. Zakai |
| Zakharov–Schulman system of equation | Acoustic waves | Vladimir E. Zakharov and E. I. Schulman |