Abstract
The weighted L q−L q (q = 1,∞) 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 \({P: L^q(\mathbb{R}^n_+) \rightarrow L^q_\sigma(\mathbb{R}^n_+)}\) (q = 1,∞) 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).
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Han, P. Weighted Decay Results for the Nonstationary Stokes Flow and Navier–Stokes Equations in Half Spaces. J. Math. Fluid Mech. 17, 599–626 (2015). https://doi.org/10.1007/s00021-015-0209-6
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DOI: https://doi.org/10.1007/s00021-015-0209-6