In this paper, we study the large-scale boundary regularity for the Stokes system in periodically oscillating John domains. Our main contribution is the construction of boundary layer correctors of arbitrary order. This is a significant generalization of the known results restricted to the first and second orders. As an application, we prove the large-scale regularity estimate, as well as a Liouville theorem, of arbitrary order for the Stokes system. Our results are also related to higher-order boundary layer tails and wall laws in viscous fluids over rough boundaries.  

　　Publication:  

　　Archive for Rational Mechanics and Analysis 247, 66 (2023).  

　　https://doi.org/10.1007/s00205-023-01899-0  

　　Author:  

　　Mitsuo Higaki  

　　Department of Mathematics, Graduate School of Science, Kobe University, 1-1 Rokkodai, Nada-ku, Kobe, 657-8501, Japan  

　　Jinping Zhuge  

　　Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China  

　　Email: jpzhuge@amss.ac.cn