On the nonstationary Stokes system in a cone

TL;DR

This paper investigates the nonstationary Stokes system within a three-dimensional cone, establishing existence, uniqueness, and regularity of solutions in weighted Sobolev spaces for the Dirichlet problem.

Contribution

It provides new mathematical results on the well-posedness and regularity of solutions to the nonstationary Stokes system in conical domains.

Findings

Existence of solutions in weighted Sobolev spaces

Uniqueness of solutions for the Dirichlet problem

Regularity properties of solutions in conical domains

Abstract

The authors consider the Dirichlet problem for the nonstationary Stokes system in a threedimensional cone. They obtain existence and uniqueness results for solutions in weighted Sobolev spaces and prove a regularity assertion for the solutions.