Geodesic
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

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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. 
@article{ZNSL_1997_249_a13,
     author = {V. A. Solonnikov},
     title = {On the estimate of maximum modulus of solution of stationary problem for the {Navier--Stokes} equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {294--302},
     publisher = {mathdoc},
     volume = {249},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_249_a13/}
}
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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/