Instabilities in Zakharov Equations for Laser Propagation in a Plasma

Details Instabilities in Zakharov Equations for Laser Propagation in a Plasma Instabilities in Zakharov Equations for Laser Propagation in a Plasma

2006-11-15

arxiv.org/abs/math/0611461v1

Dans Phase Space Analysis of Partial Differential Equations - Instabilities in Zakharov Equations for Laser Propagation in a P

Mathematics

Analysis of PDEs

Scientific paper

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.

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