SMS scnews item created by Miranda Luo at Wed 14 Dec 2022 1725
Type: Seminar
Distribution: World
Expiry: 19 Dec 2022 Calendar1: 19 Dec 2022 1500-1600 CalLoc1: Zoom webinar
Auth: miranda@w7r3b0j3.staff.wireless.sydney.edu.au (jluo0722) in SMS-SAML
Asia-Pacific Analysis and PDE Seminar
Thin-film limit of the Navier-Stokes equations in a curved thin domains
Tatsu-Hiko Miura
Dear friends and colleagues,
on Monday, 19 December 2022 at • 12:00 PM for Beijing, Hong Kong and Perth • 01:00 PM for Seoul and Tokyo • 03:00 PM for Canberra, Melbourne and Sydney • 05:00 PM for Auckland
Thin-film limit of the Navier-Stokes equations in a curved thin domains
Abstract:
We consider the incompressible Navier-Stokes equations with Navier's slip boundary conditions in a 3D curved thin domain around a given closed surface. Under suitable assumptions, we show that the average in the thin direction of a strong solution to the thin domain problem weakly converges on the closed surface as the thickness of the thin domain tends to zero. Moreover, we derive limit equations on the closed surface by characterizing the weak limit of the average as a unique weak solution to the limit equations. Our limit equations are the Navier-Stokes equations on the closed surface described in terms of a fixed coordinate system of the ambient Euclidean space. However, it turns out that they are intrinsic and agree with the Navier-Stokes equations on an abstract Riemannian manifold. We also compare our limit equations with limit equations derived by Temam and Ziane (1997) under different boundary conditions when the surface is a sphere and show that the difference in two limit equations is due to the curvature of the boundary of the curved thin domain.
Chair: Yoshikazu Giga (The University of Tokyo, Japan)
More information and how to attend this talk can be found at the
seminar webpage .
Miranda
On behalf of Daniel H. and Ben
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Webinar Speaker
Tatsu-Hiko Miura
Assistant Professor @ Hirosaki University, Japan
Tatsu-Hiko Miura received his PhD in September 2018 at the University of Tokyo under the supervision of Professor Yoshikazu Giga. He was a JSPS Research Fellow PD from 2019 to 2022. Since April 2022, he has been an Assistant Professor at Hirosaki University.