Differential and Integral Equations
- Differential Integral Equations
- Volume 11, Number 1 (1998), 95-105.
Well-posedness of the shallow water equations in the presence of a front
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.
Differential Integral Equations, Volume 11, Number 1 (1998), 95-105.
First available in Project Euclid: 1 May 2013
Permanent link to this document
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