Scientific equations named after people

This is a list of scientific equations named after people (eponymous equations).

Equation Field Person(s) named after
Allen–Cahn equation[1][2] 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
Assis-Einloft model[3][4][5] Radio wave propagation, rain attenuation Mauro S. Assis and Claudio M. Einloft
Avrami equation Phase transformation Melvin Avrami
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[6][7] 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[8]
Bridgman's thermodynamic equations		 Dimensional analysis
Thermodynamics		 Percy Williams Bridgman
Percy Williams Bridgman
Broer–Kaup–Kupershmidt equation[9] 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
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
Chaplygin's equation Transonic flow Sergey Chaplygin
Chapman–Kolmogorov equation
Chapman–Enskog equation[10]		 Probability theory
Kinetic theory		 Sydney Chapman and Andrey Kolmogorov
Sydney Chapman and David Enskog
Chebyshev equation Calculus Pafnuty Chebyshev
Churchill–Bernstein equation Heat Transfer S. W. Churchill and M. Bernstein
Clairaut's equation Calculus Alexis Clairaut
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[11]
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
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 Liquid crystals John K. Hunter and Ralph Saxton
Hunter–Zheng equation PDE 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 Turbulent flow Theodore von Kármán and L. 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[12] 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 Pierre 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
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 phenemena, 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
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
Gasdynamics
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
Sawada–Kotera equation[13] 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
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
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
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

See also

References

  1. ^ "Convergence of the Allen–Cahn equation to Brakke's motion by mean curvature". Cornell University Library. http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.jdg/1214454300. Retrieved 2009-06-27. 
  2. ^ "Thermal capacity estimates on the Allen-Cahn equation". American Mathematical Society. http://www.ams.org/tran/1999-351-06/S0002-9947-99-02399-5/home.html. Retrieved 2009-06-27. 
  3. ^ Sizun, Hervé (2005). Radio wave propagation for telecommunication applications. Springer. ISBN 3540407588, 9783540407584. http://books.google.com/books?id=Ce8e0j5vnAUC&pg=PA318&dq=assis-einloft. 
  4. ^ Fišer, Ondřej (2003). "Site Diversity Gain Estimated from Rain Rate Records". Radioengineering 12 (1). http://www.radioeng.cz/fulltexts/2003/03_01_08_11.pdf. Retrieved 2011-09-20. 
  5. ^ Assis, Mauro S.; Einloft, Claudio M.. "A simple method for estimating rain attenuation distribution". Annals of Telecommunications (Springer) 32 (11-12): 478–480. doi:10.1007/BF03003498. http://www.springerlink.com/content/r6g8n77540l4157v/. Retrieved 2011-09-20. 
  6. ^ "Spiral vortex solution of Birkhoff–Rott equation". Association for Computing Machinery. http://portal.acm.org/citation.cfm?id=96813.96852. Retrieved 2009-06-27. 
  7. ^ Majda, A. J.; Bertozzi, A. L. (2008). Vorticity and incompressible flow. Cambridge University Press. ISBN 0521639484. http://books.google.co.in/books?id=Lmcz0uwHj_8C&pg=PA363&dq=Birkhoff-Rott+equation&num=100. 
  8. ^ Tropea, C.; Yarin, A. L.; Foss, J. F. (2007). Springer handbook of experimental fluid mechanics. Springer. ISBN 3540251413. http://books.google.co.in/books?id=y0xDUAdQAlkC&pg=PA44&lpg=PA44&dq=Bridgman's+equation. 
  9. ^ Zhou, X (2007). "Variational approach to the Broer–Kaup–Kupershmidt equation". Physics Letters A 363 (1-2): 108–109. doi:10.1016/j.physleta.2006.10.083 
  10. ^ Barichello, L; Rodrigues, P.; Siewert, C. E. (2004). "On computing the Chapman–Enskog and Burnett functions". J. Quantitative Spectroscopy and Radiative Transfer 86 (1): 109–114. doi:10.1016/j.jqsrt.2003.10.001 
  11. ^ "Euler-Darboux Equation". MathWorld. http://mathworld.wolfram.com/Euler-DarbouxEquation.html. Retrieved 2009-11-14. 
  12. ^ Maslov, V. P. (1983). "The Kolmogorov-Feller equation and the probabilistic model of quantum mechanics". J. Math. Sci. (Springer) 23 (5): 2534–2553. doi:10.1007/BF01084703. ISSN 1573-8795. http://www.springerlink.com/content/k647934570142h07/. Retrieved 2009-10-25. 
  13. ^ Sawada, K.; T. Kotera (1974). "A method for finding N-soliton solutions of the KdV equation and KdV-like equation". Prog. Theor. Phys. 51 (5): 1355–1362. doi:10.1143/PTP.51.1355.