Well-posedness of the shallow water equations in the presence of a front
The article deals with the initial value problem for the inviscid, 2-dimensional shallow water equations. The first two equations express the balance of momentum involving inertial and pressure terms, with the pressure assumed hydrostatic. The third equation expresses mass conservation. This system of equations is studied in the case where a ``front'' is present, i.e., a boundary where the fluid depth is zero. Since the wave speed in shallow water behaves like square root of the depth, this results in a degenerate hyperbolic system ``on the edge'' of change of type. The local time existence of smooth solutions is proved.
local time existence of smooth solutions
scientific article; zbMATH DE number 1452493