= Unsteady Prandtl equation
{title2=$u_t+uu_x+vu_y=\mathcal U_t+\mathcal U\mathcal U_x+\nu u_{yy},\quad u_x+v_y=0$}
The unsteady form of the <Prandtl boundary-layer equation> evolves the tangential boundary-layer <velocity> under advection, outer pressure forcing and normal viscous diffusion. Incompressibility supplies the normal <velocity>. A stationary wall imposes the <no-slip boundary condition>, and tangential <velocity> matches the prescribed outer slip <velocity> far from the wall. The normal far-field disturbance need not vanish.
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