text: In reality, the Couette solution is not reached instantaneously. The "startup problem" describing the approach to steady state is given by
  subject to the initial condition
  and with the same boundary conditions as the steady flow:
  The problem can be made homogeneous by subtracting the steady solution. Then, applying separation of variables leads to the solution:
  The timescale describing relaxation to steady state is , as illustrated in the figure. The time required to reach the steady state depends only on the spacing between the plates  and the kinematic viscosity of the fluid, but not on .