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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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III.23 The Euler and Navier-Stokes Equations

Charles Feffermcm

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 Imaged, with d equal to 2 or 3. Suppose that, at position x = (x1, . . . , xd) ∈Imaged and at time t ∈ Image, the fluid is moving with a velocity ...

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