Abstract:

We consider motions to the nonhomogeneous Navier-Stokes problem in cylindrical domains in R^3, with large inflow and outflow. With "nonhomogeneous" we mean a density dependent system. The inflow and outflow are prescribed on the parts of the boundary which are perpendicular to the x_3-axis. We prove the existence of global strong solutions without smallness restrictions on velocity and flux but under assumptions that inflow and outflow are close to homogeneous and x_3 derivatives of external force and initial velocity are sufficiently small. The key step is to verify that 3-rd coordinate of velocity remains positive.