Geodesic
Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling
Mathematica Bohemica, Tome 147 (2022) no. 4, pp. 461-470

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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.
DOI : 10.21136/MB.2021.0172-20
Classification : 35G55, 35Q40
Keywords: low regularity; global well-posedness; Klein-Gordon-Schrödinger equation; higher order coupling 
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Soenjaya, Agus Leonardi. Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling. Mathematica Bohemica, Tome 147 (2022) no. 4, pp. 461-470. doi: 10.21136/MB.2021.0172-20

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