Pacific Institute for the Mathematical Sciences - PIMS

Asymptotics of small exterior Navier-Stokes flows with non-decaying boundary data

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 $t \in R$ or $t \in (0,\infty)$. In the case $t \in (0,\infty)$ 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.

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