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 $M_{rm halo}>2times10^{9}$ $h^{-1}$ 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 $zlesssim6$, and we show here that it can also predict evolution of the rest-frame far-UV luminosity function for $7lesssim zlesssim10$ 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 $zsim11$ 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 $sim5times$ greater at this redshift. Similar observations with MIRI are predicted not to detect any galaxies at $zgtrsim6$. 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.
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