Boundary value problem of a non-stationary Stokes system in a bounded smooth cylinder

TL;DR

This paper investigates the boundary value problem for the non-stationary Stokes system within a bounded smooth cylinder, extending existing results to weaker function spaces in the half-plane case as a step towards broader understanding.

Contribution

It extends Solonnikov's results on the non-stationary Stokes system to weaker function spaces in a half-plane cylinder setting.

Findings

Extended solvability results to weaker function spaces.

Analyzed boundary value problem in half-plane cylinder.

Provided foundational step for bounded smooth cylinder case.

Abstract

In this paper, we intend to study the boundary value problem of the non-stationary Stokes system in a bounded smooth cylinder $\Omega\times (0,T)$. As a first step, we consider the problem in half-plane cylinder ${\mathbb R}^n_+ \times (0,T), \,\, 0 < T \leq \infty$. We extend the result of Solonnikov\cite{So} to data in weaker function spaces than the one considered in \cite{So}.