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诸葛金平 博士:Large-scale regularity for stationary Navier-Stokes equations over non-Lipschitz boundaries

本站小编 Free考研考试/2021-12-26


Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
Speaker: 诸葛金平 博士，University of Chicago
Inviter:
Title:
 Large-scale regularity for stationary Navier-Stokes equations over non-Lipschitz boundaries
Time & Venue:
 2021.07.07 10:00-12:00 腾讯会议：304 706 305
Abstract:
 In this talk, I will discuss the large-scale boundary regularity of the stationary Navier-Stokes equations over a microscopically oscillating John boundary (with a no-slip boundary condition), which allows inward cusps or fractals. By a comprehensive large-scale analysis, we show a large-scale Lipschitz estimate for the velocity and a large-scale oscillation estimate for the pressure. By introducing the 1st-order and 2nd-order boundary layers, we also show the large-scale C^{1,alpha} and C^{2,alpha} estimates (For C^{2,alpha} estimate, we assume additionally the boundary is periodic). The proofs rely on the quantitative excess decay method developed recently in homogenization theory. This is joint work with Mitsuo Higaki and Christophe Prange.

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