$L^p$ solvability of the Stationary Stokes problem on domains with conical singularity in any dimension

TL;DR

This paper proves the solvability of the stationary Stokes problem with $L^p$ data on domains with conical singularities across a range of p-values, extending understanding of fluid flow in irregular geometries.

Contribution

It establishes $L^p$ solvability for the stationary Stokes problem on domains with conical singularities for all p in a specific range, including continuous data solutions.

Findings

Solvability for all p in (2-ε, ∞]

Existence of solutions in continuous function spaces

Extension to non-Lipschitz domains

Abstract

The Dirichlet boundary value problem for the Stokes operator with $L^p$ data in any dimension on domains with conical singularity (not necessary a Lipschitz graph) is considered. We establish the solvability of the problem for all $p\in (2-\varepsilon,\infty]$ and also its solvability in $C(\overline{D})$ for the data in $C(\partial D)$