ON LOCAL ENERGY DECAY ESTIMATE OF THE OSEEN SEMIGROUP IN TWO DIMENSIONS AND ITS APPLICATION

We study the temporal decay estimate of the Oseen semigroup in a two-dimensional exterior domain. We establish the local energy decay estimate with a suitable dependence on the small translation speed, which is a significant improvement of Hishida’s result in 2016. As an application, we prove the $L^{q}$ - $L^{r}$ estimates of the Oseen semigroup uniformly in the small translation speed.