We study the local behavior of a solution to a generalized non-stationary Stokes system with singular coefficients in (Formula presented.) with (Formula presented.). One of our main results is a bound on the vanishing order of a non-trivial solution u satisfying the generalized non-stationary Stokes system, which is a quantitative version of the (strong) unique continuation property for u. Different from the previously known results, our 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-cylinder inequalities for u.
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