Space Propagation of Instabilities in Zakharov Equations
نویسنده
چکیده
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.
منابع مشابه
Instabilities in Zakharov Equations
In [2], 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 Cauch...
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