Space Propagation of Instabilities in Zakharov Equations
arXiv:math/0703500 · doi:10.1016/j.physd.2008.03.024
Abstract
In this paper we study an initial boundary value problem for Zakharov's equations, describing the space propagation of a laser beam entering in a plasma. We prove a strong instability result and prove that the mathematical problem is ill-posed in Sobolev spaces. We also show that it is well posed in spaces of analytic functions. Several consequences for the physical consistency of the model are discussed.
39 p