Exact Solutions to the Navier-Stokes Equation

Transform Method

An alternative is to use the transform method. Taking the Laplace transform of Equation (1), it follows that

(19)

or

(20)

The solution to (20) is

(21)

Boundary conditions (2) and (3) imply that

(22)

Thus, the solution in the transform domain is given by

(23)

Inverse Laplace transform of (23) gives

(24)