On the estimate of maximum modulus of solution of stationary problem for the Navier–Stokes equations

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.