| Instability | Field | Named for |
| Benjamin–Feir instability | Surface gravity waves | T. Brooke Benjamin and Jim E. Feir |
| Buneman instability | Plasma physics | Oscar Buneman |
| Chandrasekhar–Donnelly instability | Taylor-Couette instability of Helium II | Subrahmanyan Chandrasekhar and R.J. Donnelly |
| Chandrasekhar–Friedman–Schutz instability | Instability of rotating self-gravitating mass due to gravitational radiation damping | Subrahmanyan Chandrasekhar, John L. Friedman and Bernard F. Schutz |
| Cherenkov instability | Plasma physics | Pavel Alekseevich Cherenkov |
| Chromo-Weibel instability | Plasma physics | E. S. Weibel |
| Crow instability | Aerodynamics | S. C. Crow |
| Darrieus–Landau instability | Stability of propagating flame | Georges Jean Marie Darrieus and Lev Landau |
| Dean instability | Stability of flow in a curved pipe | William Reginald Dean |
| D'yakov–Kontorovich instability | Stability of a plane shock | S. P. D'yakov and Victor M. Kontorovich |
| Faraday instability | Vibrating fluid surfaces | M. Faraday |
| Farley–Buneman instability | Plasma instability | Donald T. Farley and Oscar Buneman |
| Görtler instability | Stability of flow along a concave boundary layer | H. Görtler |
| Holmboe instability | Stratified shear flows | Jørgen Holmboe |
| Jeans instability | Stability of interstellar gas clouds | James Jeans |
| Kelvin–Helmholtz instability | Stability of shearing flow | Lord Kelvin and Hermann von Helmholtz |
| Kruskal–Shafranov instability | Plasma physics | Martin David Kruskal and Vitaly Shafranov |
| Peratt instability[1] | Plasma physics | Anthony Peratt |
| Plateau–Rayleigh instability | Stability of jets and drops | Joseph Plateau and Lord Rayleigh |
| Rayleigh–Bénard instability | Natural convection, Rayleigh–Bénard convection | Lord Rayleigh and Henri Bénard |
| Rayleigh–Taylor instability | Instability created by density stratification | Lord Rayleigh and Geoffrey Ingram Taylor |
| Richtmyer–Meshkov instability | Plasma physics, Astrophysics | R. D. Richtmyer and E. E. Meshkov |
| Roberts–Stewartson instability | Instability of rotating self-gravitating mass due to viscosity | Paul H. Roberts and Keith Stewartson |
| Saffman–Taylor instability | Flow in porous medium | Philip Saffman and Geoffrey Ingram Taylor |
| Taylor–Caulfield instability | Stratified shear flows | Geoffrey Ingram Taylor and Colm-cille P. Caulfield |
| Taylor–Couette instability | Flow in rotating cylinder | Geoffrey Ingram Taylor and Maurice Marie Alfred Couette |
| Tollmien–Schlichting instability | Wave instability in shearing flows | Walter Tollmien and Hermann Schlichting |
| Velikhov instability | Plasma physics (non-equilibrium MHD) | Evgeny Velikhov |
| Velikhov-Chandrasekhar instability | Stability of rotating fluid in magnetic field | Evgeny Velikhov and Subrahmanyan Chandrasekhar |
| Weibel instability | Plasma physics | E. S. Weibel |
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