Spatial and temporal decay estimate of the Stokes flow of weighted L1 initial data in the half space

In this paper, we derive the spatial and temporal decay estimate of the Stokes solution e−tAa in the half space when the prescribed initial data is in a weighted L1 space. We obtained that ‖xire−tAa‖L∞≤Ct−n2−12‖xirxna‖L1+Ct−n2+r−12‖xna‖L1 for 0≤r