LINEAR AND NON-LINEAR FLOW PROBLEMS AROUND OBSTACLES

We discuss the problem of the steady two-dimensional flow past fixed disturbances in an open channel of finite depth. We consider different types of obstacles, like submerged or surface-piercing bodies, and localized perturbations of a horizontal bottom; recent results on unique solvability of the linear problem and rigorous proofs of solvability of the non linear, free boundary problem are reviewed.