Weighted Decay Results for the Nonstationary Stokes Flow and Navier-Stokes Equations in Half Spaces

摘要

The weighted L-q - L-q (q = 1,infinity) estimates for the Stokes flow are given in half spaces. Further large-time weighted decays for the second spatial derivatives of the Navier-Stokes equations are established, where the unboundedness of the projection operator P : L-q(R-+(n)) -> L-sigma(q) (R-+(n)) (q = 1,infinity) is overcome by employing a decomposition for the convection term. The main results in this article are motivated by the work in Bae (J Differ Equ 222:1-20, 2006; J Math Fluid Mech 10:503-530, 2008) and Bae and Jin (Proc R Soc Edinb Sect A 135:461-477, 2005).