References & Citations
Mathematics > Analysis of PDEs
Title: Rigid Lid limit in shallow water over a flat bottom
(Submitted on 15 Dec 2023 (v1), last revised 27 Mar 2024 (this version, v3))
Abstract: We perform the so-called rigid lid limit on different shallow water models such as the abcd Bousssinesq systems or the Green-Naghdi equations. To do so we consider an appropriate nondimensionalization of these models where two small parameters are involved: the shallowness parameter {\mu} and a parameter {\epsilon} which can be interpreted as a Froude number. When parameter {\epsilon} tends to zero, the surface deformation formally goes to the rest state, hence the name rigid lid limit. We carefully study this limit for different topologies. We also provide rates of convergence with respect to {\epsilon} and a careful attention is given to the dependence on the shallowness parameter {\mu}.
Submission history
From: Benjamin Melinand [view email][v1] Fri, 15 Dec 2023 08:38:59 GMT (25kb)
[v2] Mon, 18 Dec 2023 10:44:22 GMT (26kb)
[v3] Wed, 27 Mar 2024 09:39:59 GMT (894kb)
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