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In this paper, we establish the estimates for the gradient and thesecond-order partial derivatives for the Stokes flow in the presence of twoclosely located strictly convex inclusions in dimension three. Moreover, theblow-up rate of the gradient is showed to be optimal by a pointwise upper boundand a lower bound in the narrowest region. We also show the optimal blow-uprate of Cauchy stress tensor. In dimensions greater than three, the upperbounds of the gradient are established. These results answer the questionsraised in [25].

Estimates for stress concentration between two adjacent rigid inclusions in Stokes flow