2020/02/15 by Tatsu‐Hiko Miura, Tatsu-Hiko Miura
Engineering · Mathematics · #Algorithm #Boundary (topology) #Boundary value problem #Computational Fluid Dynamics and Aerodynamics #Domain (mathematical analysis) #Geometry #Mathematical analysis #Mathematical proof #Mathematics #Mechanics #Navier-Stokes equation solutions #Navier–Stokes equations #Physics #Product (mathematics) #Residual #Slip (aerodynamics) #Stability and Controllability of Differential Equations #Thermodynamics #math.AP #msc:35Q30 #msc:76A20 #msc:76D03 #msc:76D05
paper · pdf · doi:10.1007/s00021-020-00534-2
53 pages. This paper is the second part of the divided and revised version of arXiv:1811.09816
arxiv created 2020/02/15 · openalex created_date 2020/02/24 · openalex publication_date 2020/11/23 · arxiv updated 2020/12/30 · openalex updated_date 2026/08/05
We consider the Navier-Stokes equations in a three-dimensional curved thin domain around a given closed surface under Navier's slip boundary conditions. When the thickness of the thin domain is sufficiently small, we establish the global existence of a strong solution for large data. We also show several estimates for the strong solution with constants explicitly depending on the thickness of the thin domain. The proofs of these results are based on a standard energy method and a good product estimate for the convection and viscous terms following from a detailed study of average operators in the thin direction. We use the average operators to decompose a three-dimensional vector field on the thin domain into the almost two-dimensional average part and the residual part, and derive good estimates for them which play an important role in the proof of the product estimate.