Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 29, Tome 249 (1997), pp. 294-302
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V. A. Solonnikov. On the estimate of maximum modulus of solution of stationary problem for the Navier–Stokes equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 29, Tome 249 (1997), pp. 294-302. http://geodesic.mathdoc.fr/item/ZNSL_1997_249_a13/
@article{ZNSL_1997_249_a13,
author = {V. A. Solonnikov},
title = {On the estimate of maximum modulus of solution of stationary problem for the {Navier{\textendash}Stokes} equations},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {294--302},
year = {1997},
volume = {249},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_249_a13/}
}
TY - JOUR
AU - V. A. Solonnikov
TI - On the estimate of maximum modulus of solution of stationary problem for the Navier–Stokes equations
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1997
SP - 294
EP - 302
VL - 249
UR - http://geodesic.mathdoc.fr/item/ZNSL_1997_249_a13/
LA - ru
ID - ZNSL_1997_249_a13
ER -
%0 Journal Article
%A V. A. Solonnikov
%T On the estimate of maximum modulus of solution of stationary problem for the Navier–Stokes equations
%J Zapiski Nauchnykh Seminarov POMI
%D 1997
%P 294-302
%V 249
%U http://geodesic.mathdoc.fr/item/ZNSL_1997_249_a13/
%G ru
%F ZNSL_1997_249_a13
It is shown that the solution of a nonlinear stationary problem for the Navier–Stokes equations in a bounded domain $\Omega\subset\mathbb R^3$ with the boundary conditions $\vec v\big|_{\partial\Omega}=\vec a(x)$ satisfies the inequality $$ \sup_{x\in\Omega}|\vec v(x)|\le c\Bigl(\,\sup_{x\in\partial\Omega}|\vec a(x)|\Bigr) $$ for arbitrary Reynolds number.
