Mathematica Bohemica, first online, pp. 1-10


Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling

Agus Leonardi Soenjaya

Received October 29, 2020.   Published online November 15, 2021.

Abstract:  Global well-posedness for the Klein-Gordon-Schrödinger system with generalized higher order coupling, which is a system of PDEs in two variables arising from quantum physics, is proven. It is shown that the system is globally well-posed in $(u,n)\in L^2\times L^2$ under some conditions on the nonlinearity (the coupling term), by using the $L^2$ conservation law for $u$ and controlling the growth of $n$ via the estimates in the local theory. In particular, this extends the well-posedness results for such a system in Miao, Xu (2007) for some exponents to other dimensions and in lower regularity spaces.
Keywords:  low regularity; global well-posedness; Klein-Gordon-Schrödinger equation; higher order coupling
Classification MSC:  35Q40, 35G55
DOI:  10.21136/MB.2021.0172-20

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Affiliations:   Agus Leonardi Soenjaya, Merlion School, Mathematics Department, Jl. Mayjen HR Muhammad No. 371, Surabaya 60189, Indonesia, e-mail: agus.leonards16@gmail.com


 
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