Well-posedness of the shallow water equations in the presence of a front
type: Item
instance of: scholarly article
title: Well-posedness of the shallow water equations in the presence of a front
zbMATH Open document ID: 1008.35051
author: Michael Renardy
published in: Differential and Integral Equations
publication date: 2000-05-24T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 35L80
zbMATH DE Number: 1452493
zbMATH Keywords: shallow water equations
zbMATH Keywords: balance of momentum
zbMATH Keywords: mass conservation
zbMATH Keywords: degenerate hyperbolic system
zbMATH Keywords: local time existence of smooth solutions
reviewed by: Stanislav Kračmar
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1452493