Differential and Integral Equations

Well-posedness of the shallow water equations in the presence of a front

Michael Renardy

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We consider the initial value problem for the inviscid shallow-water equations in the case where a "front" is present, i.e., a boundary where the fluid depth tends to zero. Since the wave speed in shallow water behaves like the square root of the depth, this results in a degenerate hyperbolic system "on the edge" of change of type. It is shown that smooth solutions exist for smooth initial data.

Article information

Differential Integral Equations, Volume 11, Number 1 (1998), 95-105.

First available in Project Euclid: 1 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q35: PDEs in connection with fluid mechanics
Secondary: 35L80: Degenerate hyperbolic equations 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30] 76C05


Renardy, Michael. Well-posedness of the shallow water equations in the presence of a front. Differential Integral Equations 11 (1998), no. 1, 95--105. https://projecteuclid.org/euclid.die/1367414137

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