Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

HOME ALL ARTICLES View

Commun. Korean Math. Soc. 2022; 37(3): 735-748

Online first article January 20, 2022      Printed July 31, 2022

https://doi.org/10.4134/CKMS.c210218

Copyright © The Korean Mathematical Society.

An improved global well-posedness result for the modified Zakharov equations in 1-D

Agus L. Soenjaya

Merlion School

Abstract

The global well-posedness for the fourth-order modified Zakharov equations in 1-D, which is a system of PDE in two variables describing interactions between quantum Langmuir and quantum ion-acoustic waves is studied. In this paper, it is proven that the system is globally well-posed in $(u,n)in L^2 imes L^2$ by making use of Bourgain restriction norm method and $L^2$ conservation law in $u$, and controlling the growth of $n$ via appropriate estimates in the local theory. In particular, this improves on the well-posedness results for this system in cite{GZG} to lower regularity.

Keywords: Global well-posedness, low regularity, modified Zakharov equations

MSC numbers: Primary 35Q40, 35G55

Stats or Metrics

Share this article on :

Related articles in CKMS