  We present predictions for the outcome of deep galaxy surveys with the
$James$ $Webb$ $Space$ $Telescope$ ($JWST$) obtained from a physical model of
galaxy formation in $\Lambda$CDM. We use the latest version of the GALFORM
model, embedded within a new ($800$ Mpc)$^{3}$ dark matter only simulation with
a halo mass resolution of $M_{\rm halo}>2\times10^{9}$ $h^{-1}$ M$_{\odot}$.
For computing full UV-to-mm galaxy spectral energy distributions, including the
absorption and emission of radiation by dust, we use the spectrophotometric
radiative transfer code GRASIL. The model is calibrated to reproduce a broad
range of observational data at $z\lesssim6$, and we show here that it can also
predict evolution of the rest-frame far-UV luminosity function for $7\lesssim
z\lesssim10$ which is in good agreement with observations. We make predictions
for the evolution of the luminosity function from $z=16$ to $z=0$ in all
broadband filters on the Near InfraRed Camera (NIRCam) and Mid InfraRed
Instrument (MIRI) on $JWST$ and present the resulting galaxy number counts and
redshift distributions. Our fiducial model predicts that $\sim1$ galaxy per
field of view will be observable at $z\sim11$ for a $10^4$ s exposure with
NIRCam. A variant model, which produces a higher redshift of reionization in
better agreement with $Planck$ data, predicts number densities of observable
galaxies $\sim5\times$ greater at this redshift. Similar observations with MIRI
are predicted not to detect any galaxies at $z\gtrsim6$. We also make
predictions for the effect of different exposure times on the redshift
distributions of galaxies observable with $JWST$, and for the angular sizes of
galaxies in $JWST$ bands.
