The Navier–Stokes equations (/nævˈjeɪ stoʊks/ nav-YAY STOHKS) are partial differential equations which describe the motion of viscous fluid substances...

The Navier–Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier–Stokes equations, a system of partial...

mechanics. The Navier–Stokes equations refer eponymously to him, with George Gabriel Stokes. After the death of his father in 1793, Navier's mother left...

based on Hagenbach's work. The Hagen–Poiseuille equation can be derived from the Navier–Stokes equations. The laminar flow through a pipe of uniform (circular)...

momentum equation can be derived from the Navier–Stokes equations that describe fluid motion. The x-component of the Navier–Stokes equations – when expressed...

of inviscid flow, the Navier–Stokes equation can be simplified to a form known as the Euler equation. This simplified equation is applicable to inviscid...

Continuity equations underlie more specific transport equations such as the convection–diffusion equation, Boltzmann transport equation, and Navier–Stokes equations...

death in 1903. As a physicist, Stokes made seminal contributions to fluid mechanics, including the Navier–Stokes equations; and to physical optics, with...

existence for a Monge–Ampere equation. The open problem of existence (and smoothness) of solutions to the Navier–Stokes equations is one of the seven Millennium...

Korteweg–de Vries equation Modified KdV–Burgers equation Maxwell's equations Navier–Stokes equations Poisson's equation Primitive equations (hydrodynamics)...

particular, they correspond to the Navier–Stokes equations with zero viscosity and zero thermal conductivity. The Euler equations can be applied to incompressible...

variables, similar to the Navier–Stokes equations of fluid dynamics. The derivation of the Madelung equations is similar to the de Broglie–Bohm formulation...

described by partial differential equations. For example, the Navier–Stokes equations are a set of partial differential equations derived from the conservation...

law is a special case of the Stokes equation for the momentum flux, in turn deriving from the momentum Navier-Stokes equation. Darcy's law was first determined...

root-mean-square (RMS) velocity fluctuations. In the Reynolds-averaged Navier Stokes equations, the turbulence kinetic energy can be calculated based on the closure...

advance in the mathematical theory (cf. Navier–Stokes existence and smoothness). However, if the differential equation is a correctly formulated representation...

problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills...

the dynamics of evolution equations, in particular on global attractors, perturbation theory, and the Navier-Stokes equations in thin domains. In the last...

Functional equation Functional equation (L-function) Constitutive equation Laws of science Defining equation (physical chemistry) List of equations in classical...

CFD problems is the Navier–Stokes equations, which define many single-phase (gas or liquid, but not both) fluid flows. These equations can be simplified...

governing equations obtained in this manner are called the elastostatic equations, the special case of the steady Navier–Cauchy equations given below...

concerned with nonlinear partial differential equations of hydrodynamics (Euler equation, Navier-Stokes equation, surface waves, gravity waves, capillary waves...

Sciences for his work on the Navier-Stokes equations. From 1995 to 2001 he was a member of the Institut Universitaire de France. In 1995 he was awarded...

the equations gives the Reynolds-averaged Navier–Stokes (RANS) equations, which govern the mean flow. However, the nonlinearity of the Navier–Stokes equations...

results a simplistic form for the nonlinear convective terms of the Navier-Stokes equations, at the expense of making the diffusion terms complicated. Favre...

equation in nonlinear wave motion KdV equation Magnetohydrodynamics Grad–Shafranov equation Navier–Stokes equations Euler equations Burgers' equation...

of the Reynolds Equation from the Navier-Stokes equation can be found in numerous lubrication text books. In general, Reynolds equation has to be solved...

be identical. This can be seen from inspection of the underlying Navier-Stokes equation, with geometrically similar bodies, equal Reynolds and Womersley...

important paper that founded the study of weak solutions of the Navier–Stokes equations. In the same year, he and Juliusz Schauder discovered a topological...

incompressible Navier-Stokes equations. For these mathematically rigorous results on the hydrodynamic limit of the Boltzmann equation of gas dynamics...