Convergence rates and $W^{1,p}$ estimates in homogenization theory of Stokes systems in Lipschitz domains

@article{Xu2016ConvergenceRA,
  title={Convergence rates and \$W^\{1,p\}\$ estimates in homogenization theory of Stokes systems in Lipschitz domains},
  author={Qiang Xu},
  journal={arXiv: Analysis of PDEs},
  year={2016}
}
  • Qiang Xu
  • Published 1 September 2016
  • Mathematics
  • arXiv: Analysis of PDEs
Concerned with the Stokes systems with rapidly oscillating periodic coefficients, we mainly extend the recent works in \cite{SGZWS,G} to those in term of Lipschitz domains. The arguments employed here are quite different from theirs, and the basic idea comes from \cite{QX2}, originally motivated by \cite{SZW2,SZW12,TS}. We obtain an almost-sharp $O(\varepsilon\ln(r_0/\varepsilon))$ convergence rate in $L^2$ space, and a sharp $O(\varepsilon)$ error estimate in $L^{\frac{2d}{d-1}}$ space by a… 
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