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.

中文翻译：

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浅水理论中黎曼数据的可接受条件

摘要 考虑了浅水方程，这是一种模拟长波在恒定深度不可压缩不可见流体表面传播的双曲线系统。众所周知，与该系统相关的黎曼问题的解决方案可能以黎曼数据的某些配置的干燥状态为特征。本文将从物理合理的意义上讨论浅水系统的黎曼问题出现的各种场景。特别地，将表明，如果对黎曼数据的处置做出某些物理假设，那么在黎曼问题的求解中就可以避免干态。