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arXiv · 1809.02912

Stability of hydraulic shock profiles

Zhao Yang·Kevin Zumbrun
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Abstract

We establish nonlinear $H^2\cap L^1 \to H^2$ stability with sharp rates of decay in $L^p$, $p\geq 2$, of general hydraulic shock profiles, with or without subshocks, of the inviscid Saint-Venant equations of shallow water flow, under the assumption of Evans-Lopatinsky stability of the associated eigenvalue problem. We verify this assumption numerically for all profiles, giving in particular the first nonlinear stability results for shock profiles with subshocks of a hyperbolic relaxation system.

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Zhao Yang, Kevin Zumbrun. 2018-09-09. Stability of hydraulic shock profiles. https://doi.org/10.1007/s00205-019-01422-4

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