# Asymptotics of small exterior Navier-Stokes flows with <br/><br/>non-decaying boundary data

Tuesday, February 23, 2010 - 2:00pm - 2:45pm

EE/CS 3-180

Tai-Peng Tsai (University of British Columbia)

*Keywords:*Asymptotics, Exterior flows, Navier-Stokes equations, self-similar

*Abstract:*We prove the unique existence of solutions of the 3D

incompressible

Navier-Stokes equations in an exterior domain with small

non-decaying boundary data, for all t ∈ R or t > 0. In

the case t > 0 it is coupled with a small initial data in

weak L

^{3}. If the boundary data is time-periodic, the spatial

asymptotics of the time-entire solution is given by a Landau

solution which is the same for all time. If the boundary data

is

time-periodic and the initial data is asymptotically discretely

self-similar, the solution is asymptotically the sum of a

time-periodic vector field and a forward discretely

self-similar

vector field as time goes to infinity. This is a joint work

with

Kyungkuen Kang and Hideyuki Miura.

MSC Code:

35Q30

Keywords: