Existence of solutions for models of shallow water in a basin with a degenerate varying bottom

摘要

We prove the existence of solutions for the great lake equations. These equations are obtained from the three-dimensional Euler equations in a basin with a free upper surface and a spatially varying bottom topography by taking a low aspect ratio, i. e., low wave speed and small wave amplitude expansion. These equations are rewritten in an abstract form by considering generalized Euler equations as in Levermore et al. (Indiana Univ Math J 45:479-510, 1996). This paper is an extension of Levermore et al. (Indiana Univ Math J 45:479-510, 1996), where the varying bottom was assumed to be nondegenerate. Here, we discuss the degenerate case and obtain similar results as in Levermore et al. (Indiana Univ Math J 45:479-510, 1996).