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: (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

Assistant Professor Tatsu-Hiko Miura is giving a talk in our Asia-Pacific Analysis and PDE Seminar on

Thin-film limit of the Navier-Stokes equations in a curved thin domains


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 .

On behalf of Daniel H. and Ben


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.

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