List of scientific equations named after people

This is a list of scientific equations named after people (eponymous equations).[1]

EquationFieldPerson(s) named after
Adams–Williamson equationSeismologyL. H. Adams and E. D. Williamson
Allen–Cahn equation[2][3]Phase separationS. Allen and John W. Cahn
Archard equationMaterials scienceJohn F. Archard
Arrhenius equationChemical kineticsSvante Arrhenius
Aryabhata equationNumber theoryAryabhata
Ashkin–Teller modelStatistical mechanicsEdward Teller Julius Ashkin
Avrami equationPhase transformationMelvin Avrami
Batchelor–Chandrasekhar equationTurbulenceGeorge Batchelor and Subrahmanyan Chandrasekhar
Bateman equationRadioactivityHarry Bateman
Bellman equationControl theoryRichard Bellman
Beltrami equationDifferential geometryEugenio Beltrami
Benedict–Webb–Rubin equationFluid dynamicsM. 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 equationFluid dynamicsDaniel Bernoulli
Bernoulli differential equationCalculusJacob Bernoulli
Bessel differential equationSpecial functionsFriedrich Bessel
Birch–Murnaghan equation of stateContinuum mechanicsFrancis Birch and Francis D. Murnaghan
Birkhoff–Rott equation[4][5]Fluid dynamicsGarrett Birkhoff
Black's equationElectronicsJames R. Black
Black–Scholes equationMathematical financeFischer Black and Myron Scholes
Blaney–Criddle equationAgronomyBlaney and Criddle
Boltzmann equationThermodynamicsLudwig Boltzmann
Bôcher's equationCalculusMaxime Bôcher
Borda–Carnot equationFluid dynamicsJean-Charles de Borda and Lazare Carnot
Boussinesq equationsWave mechanicsJoseph Boussinesq
Breit equationQuantum mechanicsGregory Breit
Bridgman's equation[6]
Bridgman's thermodynamic equations
Dimensional analysis
Thermodynamics
Percy Williams Bridgman
Percy Williams Bridgman
Broer–Kaup–Kupershmidt equation[7] Wave mechanicsLambertus Broer, D. J. Kaup, and B. A. Kupershmidt
Buckley–Leverett equationTwo-phase flow in porous mediaS. E. Buckley and M. C. Leverett
Burgers' equationFluid dynamicsJohannes Martinus Burgers
Cahn–Hilliard equationPhase separationJohn W. Cahn and John E. Hilliard
Callan–Symanzik equationQuantum field theoryCurtis Callan and Kurt Symanzik
Callendar–Van Dusen equationThermodynamicsHugh Longbourne Callendar and M. S. Van Dusen
Camassa–Holm equationFluid dynamicsRoberto Camassa and Darryl Holm
Carmona-Orbezo number[8] Flow electrode capacitive deionization Aranzazu Carmona-Orbezo
Carothers equationPolymer chemistryWallace 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 equationDifferential geometryErnesto Cesàro
Chandrasekhar–Page equationGeneral relativitySubrahmanyan Chandrasekhar and Page
Chaplygin's equationTransonic flowSergey Chaplygin
Chapman–Kolmogorov equation
Chapman–Enskog equation[9]
Probability theory
Kinetic theory
Sydney Chapman and Andrey Kolmogorov
Sydney Chapman and David Enskog
Chebyshev equationCalculusPafnuty Chebyshev
Chrystal's equationDifferential equationsGeorge Chrystal
Churchill–Bernstein equationHeat TransferS. W. Churchill and M. Bernstein
Clairaut's equationCalculusAlexis Clairaut
Clarke's equationCombustionJohn Frederick Clarke
Clausius–Clapeyron equationCalculusRudolf Clausius and Émile Clapeyron
Clausius–Mossotti equationPhysicsRudolf 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 equationsPopulation dynamicsAlfred J. Lotka and Vito Volterra
Conformal Killing equationTopology, Differential geometryWilhelm Killing
Darcy–Weisbach equationFluid dynamicsHenry Darcy and Julius Weisbach
Davey–Stewartson equationFluid dynamicsA. Davey and K. Stewartson
Debye–Hückel equationElectrochemistryPeter Debye and Erich Hückel
Degasperis–Procesi equationMathematical physicsAntonio Degasperis and M. Procesi
Dehn–Sommerville equationsGeometryMax Dehn and Duncan Sommerville
Diophantine equationMathematicsDiophantus of Alexandria
Dirac equation
Dirac equation in APS
Quantum mechanics
Quantum field theory
Paul Dirac
Paul Dirac
Doppler equationsWave mechanicsChristian Doppler
Drake equationCosmologyFrank Drake
Duffing equationDifferential equationsDuffing
Dym equationWave mechanicsHarry Dym
Einstein field equationsGeneral relativityAlbert Einstein
Ernst equationPDEFrederick J. Ernst
Euler equations (fluid dynamics)
Euler's equations (rigid body dynamics)
Euler–Bernoulli beam equation
Euler–Lagrange equation
Euler–Darboux equation[10]
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 equationGeology, SedimentologyFelix Maria Exner
Eyring–Polanyi equationChemical kineticsHenry Eyring and Michael Polanyi
Faddeev equationsQuantum mechanicsLudvig Faddeev
Falkner–Skan equationBoundary layer flowV. M. Falkner and S. W. Skan
Falkowich–Kármán equationTransonic flowFalkowich and Theodore von Kármán
Fenske equationDistillationMerrell Fenske
Fisher equationFinancial mathematicsIrving Fisher
Fisher's equationMathematicsRonald Fisher
Fokker–Planck equationProbability theoryAdriaan Fokker and Max Planck
Föppl–von Kármán equationsElasticityAugust Föppl and Theodore von Kármán
Fowler–Nordheim equationCondensed matter physicsRalph H. Fowler and Lothar Wolfgang Nordheim
Fredholm integral equationIntegral equationsErik Fredholm
Fresnel equationsWave opticsAugustin-Jean Fresnel
Friedmann equationsCosmologyAlexander 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 equationSuperconductivityLev 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 equationMagnetohydrodynamics, Plasma physicsH. Grad and Vitaly D. Shafranov
Green–Kubo relationsStatistical mechanicsM. S. Green and Ryogo Kubo
Gross–Pitaevskii equationCondensed matter physicsE. P. Gross and Lev P. Pitaevskii
Haaland equationFluid dynamicsS. E. Haaland
Hadamard–Rybczynski equationBubble dynamicsJacques 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 equationOrganic chemistryLouis Plack Hammett
Hankinson's equationWood scienceHankinson
Hartree equationAtomic physicsDouglas Hartree
Hartree–Fock equationQuantum chemistryDouglas Hartree and Vladimir Fock
Hasegawa–Mima equationPlasma physicsAkira Hasegawa and Kunioki Mima
Hazen–Williams equationHydraulics, IrrigationHazen and Williams
Helmholtz equationElectromagnetic radiation, Seismology, AcousticsHermann von Helmholtz
Henderson–Hasselbalch equationChemistryLawrence Joseph Henderson and Karl Albert Hasselbalch
Heun's equationCalculusKarl L. W. M. Heun
Hicks equationFluid dynamicsWilliam Mitchinson Hicks
Hill equation (biochemistry)BiochemistryArchibald Vivian Hill
Hill differential equationOrbital mechanicsGeorge William Hill
Hugoniot equationCompressible flowsPierre Henri Hugoniot
Hunter–Saxton equation
Hunter–Zheng equation
Liquid crystals
PDE
John K. Hunter and Ralph Saxton
John K. Hunter and Yuxi Zheng
Ishimori equationPDEY. Ishimori
John's equationCalculusFritz John
Johnson–Holmquist equation of stateCeramic scienceJohnson 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 equationCrystallographyAnatoli Kapustinskii
Kármán–Howarth equationTurbulenceTheodore von Kármán and Leslie Howarth
Karplus equationNuclear magnetic resonanceMartin Karplus
Kaup–Kupershmidt equationWave mechanicsD. J. Kaup and B. A. Kupershmidt
Kepler's equationAstronomyJohannes Kepler
Klein–Gordon equationQuantum field theoryOskar Klein and Walter Gordon
Kohn–Sham equationsMathematicsWalter Kohn and Lu Jeu Sham
Kolmogorov backward equationProbability distributionAndrey Kolmogorov
Kolmogorov–Feller equation[11]Probabilistic modelsAndrey Kolmogorov and William Feller
Korteweg–de Vries equationWave mechanics, SolitonsDiederik Korteweg and Gustav de Vries
Kozeny–Carman equationFluid dynamics, Unit operationsJosef Kozeny and Philip C. Carman
Krichever–Novikov equationLie algebraI. M. Krichever and Sergei Novikov
Laguerre's equationDifferential equationEdmond Laguerre
Lamm equationSedimentation theoryO. Lamm
Landau–Lifshitz equationAeroacousticsLev Landau and Evgeny Lifshitz
Landau–Lifshitz–Gilbert equationMagnetizationLev Landau, Evgeny Lifshitz, and T. L. Gilbert
Lane–Emden equationAstrophysicsJonathan Homer Lane and Robert Emden
Langevin equationStatistical physicsPaul Langevin
Laplace's equation
Laplace's tidal equations
Electromagnetism, Fluid dynamics
Fluid dynamics
Pierre-Simon Laplace
Pierre-Simon Laplace
Legendre's equationSpherical harmonicsAdrien-Marie Legendre
Leonard–Merritt formulaAstrophysicsPeter Leonard and David Merritt
Levy–Mises equationsSolid mechanicsPaul Lévy and Richard von Mises
Liénard equationDynamical systemsAlfred-Marie Liénard
Lighthill equationAeroacousticsJames Lighthill
Lindblad equationQuantum mechanicsG. Lindblad
Lin–Tsien equationPDELin and Tsien
Liñán's equationCombustionAmable Liñán
Lindley equationQueueing theoryDennis Lindley
Liouville equationsDifferential geometryJoseph Liouville
Lommel differential equationCalculusEugen von Lommel
Lorentz equationElectromagnetismHendrik Lorentz
Lorentz–Lorenz equationOpticsHendrik Lorentz and Ludvig Lorenz
Lotka–Volterra equationBiological systemsAlfred J. Lotka and Vito Volterra
Lyapunov equationControl theoryAleksandr Lyapunov
Madelung equationsQuantum mechanicsErwin Madelung
Majorana equationQuantum field theoryEttore Majorana
Manakov equationWave mechanics, Fiber opticsS. V. Manakov
Marchenko equationScattering theoryVladimir Marchenko
Mark–Houwink equationPolymer chemistryHerman Francis Mark and Houwink
Mason equationAtmospheric thermodynamicsBasil John Mason
Mason–Weaver equationSedimentation theoryMax Mason and Warren Weaver
Mathieu equationPeriodic phenomena, Parametric resonanceÉmile Léonard Mathieu
Mathisson–Papapetrou–Dixon equationsGeneral relativity, Gravitational wavesMathisson, A. Papapetrou, and G. W. Dixon
Maurer–Cartan equationLie groups, Differential geometryLudwig Maurer and Élie Joseph Cartan
Maxwell's equations
Maxwell relations
Electrodynamics
Thermodynamics
James Clerk Maxwell
James Clerk Maxwell
Mayo–Lewis equationPolymer chemistryFrank R. Mayo and Frederick M. Lewis
Michaelis–Menten equationChemical kineticsLeonor Michaelis and Maud Menten
Monge–Ampère equationCalculusGaspard Monge and André-Marie Ampère
Morison equationFluid dynamicsJ. R. Morison
Nahm equationsDifferential equationsWerner Nahm
Navier–Stokes equationsFluid dynamicsClaude-Louis Navier and George Gabriel Stokes
Nernst equationElectrochemistryWalther Nernst
Neugebauer equationsPrinting systemsHans E. J. Neugebauer
Newton–Euler equationsClassical mechanicsIsaac Newton and Leonhard Euler
Nonlinear Schrödinger equationTheoretical physicsErwin Schrödinger
Ornstein–Zernike equationStatistical mechanicsLeonard Ornstein and Frits Zernike
Painlevé equationsDifferential equationsPaul Painlevé
Orr–Sommerfeld equationFluid dynamics, Stability analysisWilliam McFadden Orr and Arnold Sommerfeld
Osipkov–Merritt modelAstrophysicsLeonid Osipkov and David Merritt
Papapetrou–Dixon equationsGeneral relativity, Gravitational wavesA. Papapetrou and G. W. Dixon
Pauli equationQuantum mechanicsWolfgang Pauli
Pell's equationNumber theoryJohn Pell
Penman equation
Penman–Monteith equation
Agronomy
Agronomy
Howard Penman
Howard Penman and J. L. Monteith
Picard–Fuchs equationCalculusCharles Émile Picard and Lazarus Fuchs
Poisson's equation
Poisson–de Rham equation
Calculus
Astrophysics
Siméon Denis Poisson
Siméon Denis Poisson and Georges de Rham
PopleNesbet equationsQuantum ChemistryJohn Pople and R. K. Nesbet
Prandtl–Glauert equationCompressible flowsLudwig Prandtl and Hermann Glauert
Price equationEvolutionary dynamics, Evolutionary biologyGeorge R. Price
Prony equationHydraulicsGaspard de Prony
Rabinovich–Fabrikant equationsChaotic systemsM. I. Rabinovich and A. L. Fabrikant
Ramanujan–Nagell equationNumber theorySrinivasa Ramanujan and Trygve Nagell
Randles–Sevcik equationCyclic voltammetryJohn Edward Brough Randles
Rankine–Hugoniot equationCompressible flowsWilliam Rankine and Pierre Henri Hugoniot
Rarita–Schwinger equationQuantum electrodynamicsWilliam Rarita and Julian Schwinger
Raychaudhuri equationGeneral relativityAmal 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 equationsTurbulent flowsOsborne Reynolds, Claude-Louis Navier, and George Stokes
Relativistic Euler equationsAstrophysics, Fluid dynamicsLeonhard Euler
Riccati equationCalculusJacopo Riccati
Richards equationHydrologyLorenzo Richards
Riemann theta function
Riemann zeta function
Riemann's differential equation
Special functions
Number theory
Differential equation
Bernhard Riemann
Bernhard Riemann
Bernhard Riemann
Rodrigues equationChromatographyAlirio E. Rodrigues
Roothaan equations or Roothaan–Hall equationsQuantum chemistryClemens Roothaan and George Hall
Sackur–Tetrode equationStatistical thermodynamicsHugo Martin Tetrode and Otto Sackur
Sagan equationCosmologyCarl Sagan
Saha–Langmuir equationQuantum mechanics, Statistical mechanicsMegh Nad Saha and Irving Langmuir
Saint-Venant equationsFluid dynamicsAdhémar Jean Claude Barré de Saint-Venant
Sakuma–Hattori equation[12]Thermal radiationFumihiro Sakuma and Susumu Hattori
Sawada–Kotera equation[13]Wave mechanicsK. Sawada and T. Kotera
Scheil–Gulliver equationMetallurgyG. H. Gulliver and E. Scheil
Schrödinger equation
Schrödinger–Newton equations
Quantum mechanics
Quantum mechanics
Erwin Schrödinger
Erwin Schrödinger and Isaac Newton
Schwinger–Dyson equationQuantum field theoryJulian Schwinger and Freeman Dyson
Screened Poisson equationPlasma physicsSiméon Denis Poisson
Seiberg–Witten equationPDENathan Seiberg and Edward Witten
Sellmeier equationOpticsW. Sellmeier
sine–Gordon equationSolitonsWalter Gordon
Slutsky equationConsumer theoryEugen Slutsky
Souders–Brown equationSeparation processesM. Souders and G. G. Brown
Starling equationFluid dynamicsErnest Starling
Stokes–Einstein equationDiffusion of particlesGeorge Gabriel Stokes and Albert Einstein
Strominger's equationsHeterotic string theoryAndrew Strominger
Stuart–Landau equationFluid dynamicsJohn Trevor Stuart and Lev Landau
SturmLiouville equationDifferential equationJacques Charles François Sturm and Joseph Liouville
Swamee–Jain equationFluid dynamicsP. K. Swamee and A. K. Jain
Swift–Hohenberg equationPattern formationJ. B. Swift and P. C. Hohenberg
Sylvester equation
Sylvester's formula
Control theory
Matrix theory
James Sylvester
James Sylvester
Taft equationPhysical organic chemistryRobert W. Taft
Tanaka equationStochastic theoryHiroshi Tanaka
Taylor–Goldstein equationFluid dynamicsG.I. Taylor and Sydney Goldstein
Torricelli's equationMechanicsEvangelista Torricelli
Tricomi equationPartial differential equationsFrancesco Tricomi
Tsiolkovsky rocket equationAstrodynamicsKonstantin Tsiolkovsky
Van Deemter's equationChromatographyJ. J. Van Deemter
Van der Pol equationDynamical systemsBalthasar van der Pol
Van der Waals equationThermodynamicsJohannes Diderik van der Waals
Van 't Hoff equationChemical thermodynamicsJacobus Henricus van 't Hoff
Verhulst equationPopulation dynamicsPierre François Verhulst
Vlasov equation
Vlasov–Poisson equation
Plasma physics
Plasma physics
Anatoly Vlasov
Anatoly Vlasov and Siméon Denis Poisson
Volterra integral equationIntegral equationsVito Volterra
Wald's equationProbability theoryAbraham Wald
Washburn's equationFlow in porous mediaEdward W. Washburn
Weber's equationDifferential equationHeinrich Friedrich Weber
Welch–Satterthwaite equationStatistics, Uncertainty analysisB. L. Welch and F. E. Satterthwaite
Wheeler–deWitt equationQuantum gravityJohn Archibald Wheeler and Bryce DeWitt
Whewell equationGeometryWilliam Whewell
Whitham equationWave mechanics, SolitonsGerald Whitham
Wiener equationBrownian motionNorbert 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 equationStochastic differential equationsM. Zakai
Zakharov–Schulman system of equationAcoustic wavesVladimir E. Zakharov and E. I. Schulman

See also

References

  1. "Reflections on the Natural History of Eponymy and Scientific Law", Donald deB. Beaver, Social Studies of Science, volume 6, number 1 (February, 1976), pages 89–98
  2. "Convergence of the Allen–Cahn equation to Brakke's motion by mean curvature". Cornell University Library. Retrieved 2009-06-27.
  3. Sowers, Richard; Wu, Jang-Mei (1999). "Thermal capacity estimates on the Allen-Cahn equation". Transactions of the American Mathematical Society. American Mathematical Society. 351 (6): 2553–2567. doi:10.1090/S0002-9947-99-02399-5. S2CID 53365869. Retrieved 2009-06-27.
  4. "Spiral vortex solution of Birkhoff–Rott equation". Association for Computing Machinery. August 1989. pp. 463–473. Retrieved 2009-06-27.
  5. Majda, A. J.; Bertozzi, A. L. (2008). Vorticity and incompressible flow. Cambridge University Press. ISBN 978-0521639484.
  6. Tropea, C.; Yarin, A. L.; Foss, J. F. (2007). Springer handbook of experimental fluid mechanics. Springer. ISBN 978-3540251415.
  7. Zhou, Xin-Wei (2007). "Variational approach to the Broer–Kaup–Kupershmidt equation". Physics Letters A. 363 (1–2): 108–109. Bibcode:2007PhLA..363..108Z. doi:10.1016/j.physleta.2006.10.083.
  8. Carmona-Orbezo, Aranzazu; Dryfe, Robert A.W. (2020-08-31). "Understanding the Performance of Flow-Electrodes for Capacitive Deionization through Hydrodynamic Voltammetry". Chemical Engineering Journal. 406: 126826. doi:10.1016/j.cej.2020.126826. ISSN 1385-8947.
  9. Barichello, L. B.; Rodrigues, P.; Siewert, C. E. (2004). "On computing the Chapman–Enskog and Burnett functions". J. Quantitative Spectroscopy and Radiative Transfer. 86 (1): 109–114. CiteSeerX 10.1.1.422.7691. doi:10.1016/j.jqsrt.2003.10.001.
  10. "Euler-Darboux Equation". MathWorld. Retrieved 2009-11-14.
  11. Maslov, V. P. (1983). "The Kolmogorov-Feller equation and the probabilistic model of quantum mechanics". J. Math. Sci. 23 (5): 2534–2553. doi:10.1007/BF01084703. ISSN 1573-8795. S2CID 122373527.
  12. F Sakuma, S Hattori, "Establishing a practical temperature standard by using a narrow-band radiation thermometer with a silicon detector", in Temperature: Its Measurement and Control in Science and Industry, vol. 5, edited by J F Schooley, New York, AIP, 421–427 (1982).
  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. Bibcode:1974PThPh..51.1355S. doi:10.1143/PTP.51.1355.
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