  The stress concentration is a common phenomenon in the study of fluid-solid
model. In this paper, we investigate the boundary gradient estimates and the
second order derivatives estimates for the Stokes flow when the rigid particles
approach the boundary of the matrix in dimension three. We classify the effect
on the blow-up rates of the stress from the prescribed various boundary data:
locally constant case and locally polynomial case. Our results hold for general
convex inclusions, including two important cases in practice, spherical
inclusions and ellipsoidal inclusions. The blow-up rates of the Cauchy stress
in the narrow region are also obtained. We establish the corresponding
estimates in higher dimensions greater than three.

Analysis of PDEs