On the uniqueness of flow in a recent tsunami model
Dynamical Systems
2011-03-15 v1 Mathematical Physics
Classical Analysis and ODEs
math.MP
Abstract
We give an elementary proof of uniqueness for the integral curve starting from the vertical axis in the phase-plane analysis of the recent model [A. Constantin, R.S. Johnson, Propagation of very long water waves, with vorticity, over variable depth, with applications to tsunamis, Fluid Dynam. Res. 40 (2008), 175--211]. Our technique can be applied easily in circumstances where the reparametrization device from [A. Constantin, A dynamical systems approach towards isolated vorticity regions for tsunami background states, Arch. Rational Mech. Anal. doi: 10.1007/s00205-010-0347-1] might lead to some serious difficulties.
Cite
@article{arxiv.1103.2470,
title = {On the uniqueness of flow in a recent tsunami model},
author = {Octavian G. Mustafa},
journal= {arXiv preprint arXiv:1103.2470},
year = {2011}
}