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VOL. 85 | 2020 Singular limit problem for the Navier–Stokes equations in a curved thin domain
Tatsu-Hiko Miura

Editor(s) Yoshikazu Giga, Nao Hamamuki, Hideo Kubo, Hirotoshi Kuroda, Tohru Ozawa

Abstract

We consider the incompressible Navier–Stokes equations with slip boundary conditions in a three-dimensional curved thin domain around a given closed surface. Under suitable assumptions on given data, we establish the convergence on the limit surface of the average in the thin direction of a strong solution to the bulk equations as the width of the curved thin domain tends to zero. Moreover, we characterize the limit as a unique weak solution to limit equations, which are the damped and weighted Navier–Stokes equations on the limit surface.

Information

Published: 1 January 2020
First available in Project Euclid: 29 December 2020

Digital Object Identifier: 10.2969/aspm/08510291

Subjects:
Primary: 35B25, 35Q30, 35R01, 76D05

Rights: Copyright © 2020 Mathematical Society of Japan

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