Instabilities in Zakharov Equations for Laser Propagation in a Plasma

Thierry Colin (1) , Guy Metivier (1)

1 IMB - Institut de Mathématiques de Bordeaux

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.

Domaines: Equations aux dérivées partielles [math.AP]

Thierry Colin, Guy Metivier. Instabilities in Zakharov Equations for Laser Propagation in a Plasma. Instabilities in Zakharov Equations for Laser Propagation in a Plasma, 2006, Pienza, Italy. pp 63--81. ⟨hal-00114025⟩