| Abstract: |
| The nonhomogeneous (density-dependent) Navier-Stokes equations are considered in a cylindrical domain in $R^3$, parallel to the $x_3$-axis with large inflow and outflow on the top and the bottom. Moreover, on the lateral part of
the cylinder the slip boundary conditions are assumed. The long-time existence of regular solutions is proved under assumptions that inflow and outflow are close to homogeneous and norms of derivatives with respect to $x_3$ of the external force and initial velocity are sufficiently small. The key point is to verify that the $x_3$-coordinate of
velocity remains positive. |
|