Singular limit problem for the Navier-Stokes equations in a curved thin domain

開催日時: 
2019/04/19 Fri 15:30 - 17:30
場所: 
3号館251号室
講演者: 
三浦 達彦
講演者所属: 
京都大学大学院理学研究科
概要: 

We consider the 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 Navier-Stokes equations converges weakly in appropriate function spaces on the closed surface as the width of the thin domain tends to zero. Moreover, we characterize the weak limit as a unique weak solution to limit equations on the closed surface, which are the damped and weighted Navier-Stokes equations on a closed surface.