Control results for a model of resonant interaction between short and long capillary-gravity waves
Abstract
The purpose of this article is the investigation of the global control properties of a coupled nonlinear dispersive system posed in the periodic domain , a system with the structure of a nonlinear Schr\"odinger equation and a nonlinear Korteweg-de Vries equation. Combining estimates derived from Bourgain spaces and using microlocal analysis we show that this system has global control properties. The main novelty of this work is twofold. One is that the global results for the nonlinear system are presented for the first time thanks to the propagation of singularities. The second one is that these propagation results are shown to a coupled dispersive system with two equations defined by differential operators with principal symbols of different orders.
Keywords
Cite
@article{arxiv.2104.12489,
title = {Control results for a model of resonant interaction between short and long capillary-gravity waves},
author = {Roberto de A. Capistrano-Filho and Ademir Pampu},
journal= {arXiv preprint arXiv:2104.12489},
year = {2023}
}
Comments
To appear on Nonlinear Differential Equations and Applications (NoDEA) - 28 pages