The Linearized 2D Inviscid Shallow Water Equations in a Rectangle:   Boundary Conditions and Well-Posedness
  We consider the linearized 2D inviscid shallow water equations in a rectangle. A set of boundary conditions is proposed which make these equations well-posed. Several different cases occur depending on the relative values of the reference velocities $(u_0,v_0)$ and reference height $\phi_0$ (sub- or super-critical flow at each part of the boundary). 
Aimin Huang and Roger Temam
math.AP