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 |
| _version_ | 1798017432908988416 |
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| author | Agus Leonardi Soenjaya |
| author_facet | Agus Leonardi Soenjaya |
| author_sort | Agus Leonardi Soenjaya |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T16:05:53Z |
| format | Article |
| id | doaj.art-2c59e11ae52a419b9a5e92b91906894b |
| institution | Directory Open Access Journal |
| issn | 0862-7959 2464-7136 |
| language | English |
| last_indexed | 2024-04-11T16:05:53Z |
| publishDate | 2022-12-01 |
| publisher | Institute of Mathematics of the Czech Academy of Science |
| record_format | Article |
| series | Mathematica Bohemica |
| spelling | doaj.art-2c59e11ae52a419b9a5e92b91906894b2022-12-22T04:14:48ZengInstitute of Mathematics of the Czech Academy of ScienceMathematica Bohemica0862-79592464-71362022-12-01147446147010.21136/MB.2021.0172-20MB.2021.0172-20Global well-posedness for the Klein-Gordon-Schrödinger system with higher order couplingAgus Leonardi SoenjayaGlobal 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.http://mb.math.cas.cz/full/147/4/mb147_4_2.pdf low regularity global well-posedness klein-gordon-schrödinger equation higher order coupling |
| spellingShingle | Agus Leonardi Soenjaya Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling Mathematica Bohemica low regularity global well-posedness klein-gordon-schrödinger equation higher order coupling |
| title | Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling |
| title_full | Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling |
| title_fullStr | Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling |
| title_full_unstemmed | Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling |
| title_short | Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling |
| title_sort | global well posedness for the klein gordon schrodinger system with higher order coupling |
| topic | low regularity global well-posedness klein-gordon-schrödinger equation higher order coupling |
| url | http://mb.math.cas.cz/full/147/4/mb147_4_2.pdf |
| work_keys_str_mv | AT agusleonardisoenjaya globalwellposednessforthekleingordonschrodingersystemwithhigherordercoupling |