Abstract or Additional Information
We consider the nonhomogeneous boundary value problem for the stationary
Navier-Stokes equations under the slip boundary conditions in a
two-dimensional bounded domain with multiple boundary components. By the
incompressibility condition of the fluid, the total flux of the given
boundary datum through the boundary must be zero. It is shown that this
problem admits at least one weak solution if the friction coefficient is
sufficiently large compared with the kinematic viscosity constant and
the curvature of the boundary. No additional assumption (other than the
necessary requirement of zero total flux through the boundary) is
imposed on the boundary datum. This talk is based on the joint work with
Prof. Giovanni P. Galdi (University of Pittsburgh).