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We consider the linearized 2D inviscid shallow water equations in arectangle. A set of boundary conditions is proposed which make these equationswell-posed. Several different cases occur depending on the relative values ofthe reference velocities $(u_0,v_0)$ and reference height $\phi_0$ (sub- orsuper-critical flow at each part of the boundary).

The Linearized 2D Inviscid Shallow Water Equations in a Rectangle: Boundary Conditions and Well-Posedness