Ill-posedness for the Zakharov system with generalized nonlinearity
@inproceedings{Biagioni2003IllposednessFT, title={Ill-posedness for the Zakharov system with generalized nonlinearity}, author={Hebe de Azevedo Biagioni and Felipe Linares}, year={2003} }
We study the ill-posedness question for the one-dimensional Zakharov system and a generalization of it in one and higher dimensions. Our point of reference is the criticality criteria introduced by Ginibre, Tsutsumi and Velo (1997) to establish local well-posedness.
5 Citations
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This work is concerned with the Cauchy problem for a Zakharov system with initial data in Sobolev spaces $H^k(\mathbb R^d)\!\times\!H^l(\mathbb R^d)\!\times\!H^{l-1}\!(\mathbb R^d)$. We recall the…
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<p style='text-indent:20px;'>The Zakharov system in dimension <inline-formula><tex-math id="M1">\begin{document}$ d\leqslant 3 $\end{document}</tex-math></inline-formula> is shown to be locally…
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