Geodesic
On the $(x,t)$ asymptotic properties of solutions of the Navier–Stokes equations in the half-space
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 36, Tome 318 (2004), pp. 147-202 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the space-time asymptotic behavior of classical solutions of the initial boundary value problem for the Navier–Stokes system in the half-space. We construct a (local in time) solution corresponding to an initial data assumed only continuous and decreasing at infinity as $|x|^{-\mu}$, $\mu\in(\frac12,n)$. We prove pointwise estimates in the space variable. Moreover, if $\mu\in[1,n)$ and the initial data is suitably small, the above solutions in global (in time) and we prove space-time pointwise estimates. 
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F. Crispo; P. Maremonti. On the $(x,t)$ asymptotic properties of solutions of the Navier–Stokes equations in the half-space. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 36, Tome 318 (2004), pp. 147-202. http://geodesic.mathdoc.fr/item/ZNSL_2004_318_a8/

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