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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{ZNSL_2004_318_a8,
     author = {F. Crispo and P. Maremonti},
     title = {On the $(x,t)$ asymptotic properties of solutions of the {Navier--Stokes} equations in the half-space},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {147--202},
     publisher = {mathdoc},
     volume = {318},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_318_a8/}
}
TY  - JOUR
AU  - F. Crispo
AU  - P. Maremonti
TI  - On the $(x,t)$ asymptotic properties of solutions of the Navier--Stokes equations in the half-space
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2004
SP  - 147
EP  - 202
VL  - 318
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2004_318_a8/
LA  - en
ID  - ZNSL_2004_318_a8
ER  - 
%0 Journal Article
%A F. Crispo
%A P. Maremonti
%T On the $(x,t)$ asymptotic properties of solutions of the Navier--Stokes equations in the half-space
%J Zapiski Nauchnykh Seminarov POMI
%D 2004
%P 147-202
%V 318
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2004_318_a8/
%G en
%F ZNSL_2004_318_a8
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/