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This paper is devoted to study the cost of the null controllability for theStokes system. Using the control transmutation method we show that the cost ofdriving 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 aresistance term, which will be done under assumptions on the control region.

A hyperbolic system and the cost of null controllability for the Stokes system