Homogenization of a linear nonstationary Navier–Stokes equations system with a time-variant domain with a fine-grained boundary

The problem of distortion of viscous incompressible fluid with a great number of solid particles with given velocities is considered. The diameters of particles and the distance between them tend to zero, and the number of particles tends to infinity. The asymptotic behavior of the solutions of the linear system of Navier-Stokes equations is considered. In a homogenized model there appears an additional term containing the strength tensor of a single particle.