# 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

Ill-Posedness for the Benney system

- Mathematics
- 2006

We discuss ill-posedness issues for the initial value problem
associated to the Benney system. To prove our results we use the
method introduced by Kenig, Ponce and Vega [10] to show
ill-posedness…

Norm inflation for the Zakharov system

- Mathematics
- 2022

. We prove norm inﬂation in new regions of Sobolev regularities for the scalar Zakharov system in the spatial domain R d for arbitrary d ∈ N . To this end, we apply abstract considerations of…

A Note on $C^2$ Ill-Posedness Results for the Zakharov System in Arbitrary Dimension

- Mathematics
- 2019

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…

Local well-posedness for the Zakharov system in dimension d ≤ 3

- MathematicsDiscrete & Continuous Dynamical Systems
- 2021

<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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