Question

Write the Navier-Stokes equation and explain the terms.

Answer 1

The Navier-Stokes equation, in modern notation, is , where u is the fluid velocity vector, P is the fluid pressure, ρ is the fluid density, υ is the kinematic viscosity, and ∇2 is the Laplacian operator (see Laplace's equation)



Partial results. The Navier–Stokes problem in two dimensions has already been solved positively since the 1960s: there exist smooth and globally defined solutions. ... Jean Leray in 1934 proved the existence of so-called weak solutions to the Navier–Stokes equations, satisfying the equations in mean value, not pointwise.