  We report on non-linear transport phenomena at high filling factor and DC
current-induced electronic hydrodynamics in an ultra-high mobility (mu=20x10^6
cm^2/Vs) two-dimensional electron gas in a narrow (15 micron wide) GaAs/AlGaAs
Hall bar for DC current densities reaching 0.67 A/m. The various phenomena and
the boundaries between the phenomena are captured together in a two-dimensional
differential resistivity map as a function of magnetic field (up to 250 mT) and
DC current. This map, which resembles a phase diagram, demarcate distinct
regions dominated by Shubnikov-de Haas (SdH) oscillations (and phase inversion
of these oscillations) around zero DC current; negative magnetoresistance and a
double-peak feature (both ballistic in origin) around zero field; and Hall
field-induced resistance oscillations (HIROs) radiating out from the origin.
From a detailed analysis of the data near zero field, we show that increasing
the DC current suppresses the electron-electron scattering length that drives a
growing hydrodynamic contribution to both the differential longitudinal and
transverse (Hall) resistivities. Our approach to induce hydrodynamics with DC
current differs from the more usual approach of changing the temperature. We
also find a significant (factor of two to four) difference between the quantum
lifetime extracted from SdH oscillations, and the quantum lifetime extracted
from HIROs. In addition to observing HIRO peaks up to the seventh order, we
observe an unexpected HIRO-like feature close to mid-way between the
first-order and the second-order HIRO maxima at high DC current.
