# 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} }

## 23 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…

Cauchy problem of the generalized Zakharov type system in R2$\mathbf{R}^{2}$

- MathematicsJournal 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 existence and uniqueness of smooth solution for a generalized Zakharov equation

- Mathematics
- 2010

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

- MathematicsNumerical 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

- 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…

Approximation to the global solution of generalized Zakharov equations in R2$\mathbf{R}^{2}$

- MathematicsJournal 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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