= Linearized unsteady Prandtl equation
{title2=$\tilde u_t+U\tilde u_x+V\tilde u_y+U_x\tilde u+U_y\tilde v=\nu\tilde u_{yy}$}
For a fixed outer pressure and slip <velocity>, retain terms linear in a disturbance of a base flow $(U,V)$. The tangential equation has the displayed form and continuity is $\tilde u_x+\tilde v_y=0$. Disturbances vanish at the wall and the tangential disturbance vanishes in the far field. A local parallel-profile approximation may freeze the coefficients even when the profile is not an exact global steady solution.
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