%0 Journal Article %T Space Propagation of Instabilities in Zakharov Equations %A Guy Metivier %J Mathematics %D 2007 %I arXiv %R 10.1016/j.physd.2008.03.024 %X 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. %U http://arxiv.org/abs/math/0703500v1