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In this paper we study the local behavior of a solution to the Stokes systemwith singular coefficients. One of the main results is the bound on thevanishing order of a nontrivial solution to the Stokes system, which is aquantitative version of the strong unique continuation property. Our proofrelies on some delicate Carleman-type estimates. We first use these estimatesto derive crucial \emph{optimal} three-ball inequalities. Taking advantage ofthe optimality, we then derive an upper bound on the vanishing order of anynontrivial solution to the Stokes system from those three-ball inequalities.

Optimal three-ball inequalities and quantitative uniqueness for the Stokes system