  This paper is devoted to study the cost of the null controllability for the
Stokes system. Using the control transmutation method we show that the cost of
driving the Stokes system to rest at time T is of order e^C/T when T
-->0^+,i.e., the same order as for the heat equation. For this to be possible,
we are led to study the exact controllability of one hyperbolic system with a
resistance term, which will be done under assumptions on the control region.
