Space Propagation of Instabilities in Zakharov Equations

Details Space Propagation of Instabilities in Zakharov Equations Space Propagation of Instabilities in Zakharov Equations

2007-03-16

arxiv.org/abs/math/0703500v1

Mathematics

Analysis of PDEs

39 p

Scientific paper

10.1016/j.physd.2008.03.024

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.

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