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### Open Access Journals

DCDS

We study the local behavior of a solution to the
Stokes system with singular coefficients in $R^n$ with $n=2,3$. One
of our main results is a bound on the vanishing order of a
nontrivial solution $u$ satisfying the Stokes system, which is a
quantitative version of the strong unique continuation property for
$u$. Different from the previous known results, our strong unique
continuation result only involves the velocity field $u$. Our proof
relies on some delicate Carleman-type estimates. We first use these
estimates to derive crucial

*optimal*three-ball inequalities for $u$. Taking advantage of the optimality, we then derive an upper bound on the vanishing order of any nontrivial solution $u$ to the Stokes system from those three-ball inequalities. As an application, we derive a minimal decaying rate at infinity of any nontrivial $u$ satisfying the Stokes equation under some a priori assumptions.## Year of publication

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