Inviscid, zero Froude number limit of the viscous shallow water system

Abstract

In this paper, we study the inviscid and zero Froude number limits of the viscous shallow water system. We prove that the limit system is represented by the incompressible Euler equations on the whole space. Furthermore, the rate of convergence is also obtained.

Keywords

• viscous shallow water equations
• incompressible euler equations
• low froude number limit
• inviscid limit
• 35b25
• 35q35
• 76b15