Separation points of the Stokes equations with localized boundary data in the half space
ABSTRACT
We investigate the unsteady Stokes system in the half-space with boundary data that are localized in both space and time. We prove that certain boundary influxes can generate flow reversal in the interior of the half-space, meaning that at least one component of the velocity field changes sign. Our analysis is based on the representation formula for the half-space Stokes system and on pointwise estimates derived from the Green tensor associated with non-homogeneous boundary data. Using these tools, we construct solutions whose tangential velocity components experience at least one sign change. We further show that these solutions exhibit boundary separation at the boundary.
