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.
Agus L. Soenjaya
Merlion School
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
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