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http://dx.doi.org/10.4134/CKMS.c210218

AN IMPROVED GLOBAL WELL-POSEDNESS RESULT FOR THE MODIFIED ZAKHAROV EQUATIONS IN 1-D  

Soenjaya, Agus L. (Pre-University Mathematics Department Merlion School)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.3, 2022 , pp. 735-748 More about this Journal
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 ionacoustic waves is studied. In this paper, it is proven that the system is globally well-posed in (u, n) ∈ L2 × L2 by making use of Bourgain restriction norm method and L2 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 [9] to lower regularity.
Keywords
Global well-posedness; low regularity; modified Zakharov equations;
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