Stokes drag of oscillation sphere

[chaosma]

If we consider a sphere oscillates in viscous fluid with frequency w,
then sphere has velocity u=[itex]u_0*e^{-iwt}[/itex]

In Laudau's book, he defined the velocity of fluid is:
v=[itex]e^{iwt}*F[/itex]
where F is a vector with only spatial variable involved.
The boundary condition then becomes [itex]u=v[/itex] at [itex]|x|=R[/itex],
where R is radius of sphere and origin is center of sphere.

My question is that this is a non-inertial frame, but Landau didn't introduce any
extra periodic force. Why is this true? Thank you!

 

[chaosma]

I figured it out.
First, use non-inertial frame, write down the NS equation with velocity w.
Then let [itex]u=w+u_0[/itex]
where [itex]u_0[/itex] is velocity of sphere.