Convergence Rates of Neumann problems for Stokes Systems

TL;DR

This paper investigates how quickly solutions to Neumann problems for Stokes systems with oscillating periodic coefficients converge in $L^2$ and $H^1$ norms, without requiring smoothness of the coefficients.

Contribution

It establishes convergence rates for Neumann problems of Stokes systems with oscillating coefficients without smoothness assumptions.

Findings

Established $L^2$ and $H^1$ convergence rates.

Analyzed systems with rapidly oscillating periodic coefficients.

No smoothness assumptions on coefficients.

Abstract

This paper studies the convergence rates in $L^2$ and $H^1$ of Neumann problems for Stokes systems with rapidly oscillating periodic coefficients, without any smoothness assumptions on the coefficients.