  Motivated by experiments on a hydrodynamic regime in electron transport, we
study the effect of an oscillating electric field in such a setting. We
consider a long two-dimensional channel of width $L$, whose geometrical
simplicity allows an analytical study as well as hopefully permitting
experimental realisation. The response depends on viscosity $\nu$, driving
frequency, $\omega$ and ohmic heating coefficient $\gamma$ via the
dimensionless complex variable $\frac{L^2}{\nu}(i\omega +\gamma)=i\Omega
+\Sigma$. While at small $\Omega$, we recover the static solution, a new regime
appears at large $\Omega$ with the emergence of a boundary layer. This includes
a splitting of the location of maximal flow velocity from the centre towards
the edges of the boundary layer, an an increasingly reactive nature of the
response, with the phase shift of the response varying across the channel. The
scaling of the total optical conductance with $L$ differs between the two
regimes, while its frequency dependence resembles a Drude form throughout, even
in the complete absence of ohmic heating, against which, at the same time, our
results are stable. Current estimates for transport coefficients in graphene
and delafossites suggest that the boundary layer regime should be
experimentally accessible.
