  We calculate the backflow current around a fixed impurity in a Fermi liquid.
The leading contribution at long distances is radial and proportional to 1/r^2.
It is caused by the current induced density modulation first discussed by
Landauer. The familiar 1/r^3 dipolar backflow obtained in linear response by
Pines and Nozieres is only the next to leading term, whose strength is
calculated here to all orders in the scattering. In the charged case the
condition of perfect screening gives rise to a novel sum rule for the phase
shifts. Similar to the behavior in a classical viscous liquid, the friction
force is due only to the leading contribution in the backflow while the dipolar
term does not contribute.
