Instabilities in Zakharov Equations for Laser Propagation in a Plasma
Analysis of PDEs
2007-12-12 v1
Abstract
F.Linares, G.Ponce, J-C.Saut have proved that a non-fully dispersive Zakharov system arising in the study of Laser-plasma interaction, is locally well posed in the whole space, for fields vanishing at infinity. Here we show that in the periodic case, seen as a model for fields non-vanishing at infinity, the system develops strong instabilities of Hadamard's type, implying that the Cauchy problem is strongly ill-posed.
Keywords
Cite
@article{arxiv.math/0611461,
title = {Instabilities in Zakharov Equations for Laser Propagation in a Plasma},
author = {Thierry Colin and Guy Metivier},
journal= {arXiv preprint arXiv:math/0611461},
year = {2007}
}