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

@article{Sanwal2021LocalWF, title={Local well-posedness for the Zakharov system in dimension d ≤ 3}, author={Akansha Sanwal}, journal={Discrete \& Continuous Dynamical Systems}, year={2021} }

<p style='text-indent:20px;'>The Zakharov system in dimension <inline-formula><tex-math id="M1">\begin{document}$ d\leqslant 3 $\end{document}</tex-math></inline-formula> is shown to be locally well-posed in Sobolev spaces <inline-formula><tex-math id="M2">\begin{document}$ H^s \times H^l $\end{document}</tex-math></inline-formula>, extending the previously known result. We construct new solution spaces by modifying the <inline-formula><tex-math id="M3">\begin{document}$ X^{s,b} $\end{document…

## 3 Citations

### 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…

### Global well-posedness and scattering for the Zakharov system at the critical space in three spatial dimensions with small and radial initial data

- MathematicsJournal of Mathematical Analysis and Applications
- 2022

### Local Well-Posedness of a System Describing Laser-Plasma Interactions

- MathematicsVietnam Journal of Mathematics
- 2022

A degenerate Zakharov system arises as a model for the description of laser-plasma interactions. It is a coupled system of a Schrödinger and a wave equation with a non-dispersive direction. In this…

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