Equations · equation
Navier–Stokes Equations
Fluid Dynamics · 1822
- Equation
- ρ(∂v/∂t + v·∇v) = −∇p + μ∇²v + f
- Field
- Fluid Dynamics
- Named After
- Claude-Louis Navier · George Gabriel Stokes
- Symbols
- ρ density · v velocity field · p pressure · μ viscosity · f body forces such as gravity · v·∇v the nonlinear term that makes turbulence
- Year
- 1822
Significance
Newton's second law written for flowing matter — weather, ocean currents, aerodynamics, and blood flow all obey it. Its nonlinear term breeds turbulence, and whether smooth solutions always exist remains a Clay Millennium Problem with a million dollars unclaimed.
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