Admissibility conditions for Riemann data in shallow water theory

Abstract

Consideration is given to the shallow-water equations, a hyperbolic system modeling the propagation of long waves at the surface of an incompressible inviscible fluid of constant depth. It is well known that the solution of the Riemann problem associated to this system may feature dry states for some configurations of the Riemann data. This article will discuss various scenarios in which the Riemann problem for the shallow water system arises in a physically reasonable sense. In particular, it will be shown that if certain physical assumptions on the disposition of the Riemann data are made, then dry states can be avoided in the solution of the Riemann problem.