<p>Electron hydrodynamics features a plethora of effects where electrons behave like a fluid. Its description relies on hydrodynamic models akin to the Navier-Stokes equations, which progressively lose accuracy when approaching the ballistic regime. In this paper, we derive a generalized Navier-Stokes differential equation with suitable boundary conditions for the drift velocity field in a channel. It still admits a closed-form solution in a uniform channel while spanning the range of validity of hydrodynamic models. It also includes electron tomographic dynamics, a realistic description of electron-electron collisions that affect electrical transport, and explains the occurrence of positive and negative magnetoresistance at low magnetic fields. The model describes phenomena missed by the conventional electron hydrodynamic description, and it generally improves its accuracy.</p>