III.23 The Euler and Navier-Stokes Equations
The Euler and Navier-Stokes equations describe the motion of an idealized fluid. They are important in science and engineering, yet they are very poorly understood. They present a major challenge to mathematics.
To state the equations we work in Euclidean space d, with d equal to 2 or 3. Suppose that, at position x = (x1, . . . , xd) ∈d and at time t ∈ , the fluid is moving with a velocity ...