Equations for fluid flow with friction were developed by Claude-Louis Navier and George Gabriel Stokes.

* August 21 – Claude-Louis Navier, French engineer and physicist ( b. 1785 )

* February 10 – Claude-Louis Navier, French engineer and physicist ( d. 1836 )

In physics, the Navier – Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances.

* Emiland Gauthey, civil engineer, desginger of bridges, canals and roads, uncle of Claude-Louis Navier

* Claude-Louis Navier, engineer and physicist, known for Navier-Stokes equations

* 1826: Claude-Louis Navier published a treatise on the elastic behaviors of structures

Mathematicians and Physicists who established the foundations of this aero-thermo domain include: Sir Isaac Newton, Daniel Bernoulli, Leonard Euler, Claude-Louis Navier, Sir George Gabriel Stokes, Ernst Mach, Nikolay Yegorovich Zhukovsky, Martin Wilhelm Kutta, Ludwig Prandtl, Theodore von Kármán, Paul Richard Heinrich Blasius, and Henri Coandă.

* Claude-Louis Navier

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Further mathematical justification was provided by Claude-Louis Navier and George Gabriel Stokes in the Navier – Stokes equations, and boundary layers were investigated ( Ludwig Prandtl, Theodore von Kármán ), while various scientists such as Osborne Reynolds, Andrey Kolmogorov, and Geoffrey Ingram Taylor advanced the understanding of fluid viscosity and turbulence.

Claude-Louis Bernier ( 1755 – 1830 ) was a third member of their team.

* Claude-Louis Mathieu ( 1783 – 1875 ), French mathematician and astronomer

The Navier – Stokes equations ( named after Claude-Louis Navier and George Gabriel Stokes ) are the set of equations that describe the motion of fluid substances such as liquids and gases.

With the French chemists Claude-Louis Berthollet, Antoine Fourcroy and Guyton de Morveau, Lavoisier devised a systematic chemical nomenclature.

** Histoire de l ' astronomie au dix-huitième siècle, edited by Claude-Louis Mathieu, Paris: Bachelier ( successeur de M < sup > me </ sup > V < sup > e </ sup > Courcier ), 1827. lii, 796 p., 3 folded plates.

Soon after its foundation, and after son Claude-Louis joined Moët et Cie, the winery's clientele included nobles and aristocrats.

The president of FISU is currently Claude-Louis Gallien.

* Navier – Stokes existence and smoothness

The behavior of fluids can be described by the Navier – Stokes equations — a set of partial differential equations which are based on:

By the 1920s Lewis Fry Richardson's interest in weather prediction led him to propose human computers and numerical analysis to model the weather ; to this day, the most powerful computers on Earth are needed to adequately model its weather using the Navier – Stokes equations.

Application of the viscous shear stresses to Newton's second law for an airflow results in the Navier – Stokes equations.

A similar differentiation is made in the Navier – Stokes equations.

The Navier – Stokes equations in their full and simplified forms help with the design of aircraft and cars, the study of blood flow, the design of power stations, the analysis of pollution, and many other things.

The Navier – Stokes equations are also of great interest in a purely mathematical sense.

These are called the Navier – Stokes existence and smoothness problems.

The Navier – Stokes equations dictate not position but rather velocity.

A solution of the Navier – Stokes equations is called a velocity field or flow field, which is a description of the velocity of the fluid at a given point in space and time.

The Navier – Stokes equations are nonlinear partial differential equations in almost every real situation.

It is believed, though not known with certainty, that the Navier – Stokes equations describe turbulence properly.

The numerical solution of the Navier – Stokes equations for turbulent flow is extremely difficult, and due to the significantly different mixing-length scales that are involved in turbulent flow, the stable solution of this requires such a fine mesh resolution that the computational time becomes significantly infeasible for calculation ( see Direct numerical simulation ).

To counter this, time-averaged equations such as the Reynolds-averaged Navier – Stokes equations ( RANS ), supplemented with turbulence models, are used in practical computational fluid dynamics ( CFD ) applications when modeling turbulent flows.

Another technique for solving numerically the Navier – Stokes equation is the Large eddy simulation ( LES ).

Together with supplemental equations ( for example, conservation of mass ) and well formulated boundary conditions, the Navier – Stokes equations seem to model fluid motion accurately ; even turbulent flows seem ( on average ) to agree with real world observations.

The Navier – Stokes equations assume that the fluid being studied is a continuum ( it is infinitely divisible and not composed of particles such as atoms or molecules ), and is not moving at relativistic velocities.

At very small scales or under extreme conditions, real fluids made out of discrete molecules will produce results different from the continuous fluids modeled by the Navier – Stokes equations.

Time tested formulations exist for common fluid families, but the application of the Navier – Stokes equations to less common families tends to result in very complicated formulations which are an area of current research.

The derivation of the Navier – Stokes equations begins with an application of Newton's second law: conservation of momentum ( often alongside mass and energy conservation ) being written for an arbitrary portion of the fluid.

A very significant feature of the Navier – Stokes equations is the presence of convective acceleration: the effect of time independent acceleration of a fluid with respect to space.