  We study the hydrodynamic viscous electronic transport in a two-dimensional
sample separated into two semi-infinite planes by a one-dimensional infinite
barrier. The semi-infinite planes are electrically connected via the
finite-size slit in the barrier. We calculate the current through the slit
assuming finite voltage drop between the planes and neglecting disorder-induced
Ohmic resistance, so that dissipation and resistance are purely
viscosity-induced. We find that the only solution to the Stokes equation in
this geometry, which yields a finite dissipation at finite resistance (and,
hence, is not self-contradictory), is the one that fulfills both the no-stress
and no-slip boundary conditions simultaneously. As a remarkable consequence,
the obtained velocity profile satisfies the so-called "partial-slip" (Maxwell)
boundary condition for any value of the slip length, which drops out from all
final results. We also calculate the electronic temperature profile for the
small and large heat conductivity, and find asymmetric (with respect to the
barrier) temperature patterns in the former case.
