Pointwise estimates for Green's kernel of a mixed boundary value problem to the Stokes system in a polyhedral cone

TL;DR

This paper establishes regularity results and pointwise estimates for Green's matrix of the Stokes system in a polyhedral cone with mixed boundary conditions, advancing understanding of fluid flow near complex boundaries.

Contribution

It provides new regularity results and pointwise Green's function estimates for the Stokes system in polyhedral cones with mixed boundary conditions.

Findings

Regularity results for weak solutions in weighted Sobolev spaces

Pointwise estimates for Green's matrix in polyhedral cones

Analysis of mixed boundary conditions on boundary sides

Abstract

The paper deals with a mixed boundary value problem for the Stokes system in a polyhedral cone. Here different boundary conditions (in particular, Dirichlet, Neumann, free surface conditions) are prescribed on the sides of the polyhedron. The authors obtain regularity results for weak solutions in weighted $L_2$ Sobolev spaces and prove point estimates of Green's matrix.