# An improved local well-posedness result for the one-dimensional Zakharov system

@article{Pecher2006AnIL,
title={An improved local well-posedness result for the one-dimensional Zakharov system},
author={Hartmut Pecher},
journal={Journal of Mathematical Analysis and Applications},
year={2006},
volume={342},
pages={1440-1454}
}
• H. Pecher
• Published 27 November 2006
• Mathematics
• Journal of Mathematical Analysis and Applications
23 Citations
Norm inflation for the Zakharov system
. 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
Cauchy problem of the generalized Zakharov type system in R2$\mathbf{R}^{2}$
• Mathematics
Journal of inequalities and applications
• 2017
It is proved the existence and uniqueness of global smooth solutions to the initial value problem in the Sobolev space through making a priori integral estimates and the Galerkin method.
On the global existence and small dissipation limit for generalized dissipative Zakharov system
• Mathematics
• 2018
This paper deals with the existence and uniqueness of the global solutions to the initial boundary value problem for a generalized Zakharov system with direct self‐interaction of the dispersive waves
Control of error in the homotopy analysis of solutions to the Zakharov system with dissipation
• Mathematics
Numerical Algorithms
• 2012
The method of homotopy analysis is applied to the Zakharov system with dissipation to obtain analytical solutions, treating the auxiliary linear operator as a time evolution operator and constructing approximate solutions which depend on the convergence control parameters.
The Time-Periodic Solutions to the Modified Zakharov Equations with a Quantum Correction
• Mathematics
• 2017
This paper investigates the existence and uniqueness of time-periodic solutions of the periodic initial value problem for the modified Zakharov equations with a quantum correction. By combining a
Local well-posedness for the Zakharov system in dimension d ≤ 3
• A. Sanwal
• Mathematics
Discrete & 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
Approximation to the global solution of generalized Zakharov equations in R2$\mathbf{R}^{2}$
• Shujun You
• Mathematics
Journal of inequalities and applications
• 2018
It is obtained that the solutions of the two-dimensional generalized Zakharov equations converge as α→0$\alpha\to0$ to a solution of the Zakarov equations.
Initial boundary value problem for generalized Zakharov equations with nonlinear function terms
• Mathematics
• 2020
In this paper, we consider the initial boundary value problem for generalized Zakharov equations. Firstly, we prove the existence and uniqueness of the global smooth solution to the problem by a

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