Abstract
In [LPS], F. Linares, G. Ponce and 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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© 2006 Birkhäuser Boston
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Colin, T., Métivier, G. (2006). Instabilities in Zakharov equations for laser propagation in a plasma. In: Bove, A., Colombini, F., Del Santo, D. (eds) Phase Space Analysis of Partial Differential Equations. Progress in Nonlinear Differential Equations and Their Applications, vol 69. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4521-2_6
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DOI: https://doi.org/10.1007/978-0-8176-4521-2_6
Publisher Name: Birkhäuser Boston
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Online ISBN: 978-0-8176-4521-2
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