  Hydrodynamic electron flow is experimentally observed in the differential
resistance of electrostatically defined wires in the two-dimensional electron
gas in (Al,Ga)As heterostructures. In these experiments current heating is used
to induce a controlled increase in the number of electron-electron collisions
in the wire. The interplay between the partly diffusive wire-boundary
scattering and the electron-electron scattering leads first to an increase and
then to a decrease of the resistance of the wire with increasing current. These
effects are the electronic analog of Knudsen and Poiseuille flow in gas
transport, respectively. The electron flow is studied theoretically through a
Boltzmann transport equation, which includes impurity, electron-electron, and
boundary scattering. A solution is obtained for arbitrary scattering
parameters. By calculation of flow profiles inside the wire it is demonstrated
how normal flow evolves into Poiseuille flow. The boundary-scattering
parameters for the gate-defined wires can be deduced from the magnitude of the
Knudsen effect. Good agreement between experiment and theory is obtained.
