Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling
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 nonlin...
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2022-12-01
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| Series: | Mathematica Bohemica |
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| Online Access: | http://mb.math.cas.cz/full/147/4/mb147_4_2.pdf |
| Summary: | 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. |
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| ISSN: | 0862-7959 2464-7136 |