On time-periodic Navier-Stokes flows with fast spatial decay in the whole space

摘要

We investigate the pointwise behavior of time-periodic Navier-Stokes flows in the whole space. We show that if the time-periodic external force is sufficiently small in an appropriate sense, then there exists a unique time-periodic solution {u, p} of the Navier-Stokes equation such that |u(t, x)| = O(|x|~(1-n)),|?u(t, x)| = O(|x|~(-n)) and |p(t, x)| = O(|x|~(-n)) uniformly in t ∈ R as |x| → ∞. Our solution decays more rapidly than the time-periodic Stokes fundamental solution. The proof is based on the representation formula of a solution via the time-periodic Stokes fundamental solution and its properties.