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

Agus Leonardi Soenjaya

Mathematica Bohemica (2022)

  • Volume: 147, Issue: 4, page 461-470
  • ISSN: 0862-7959

Abstract

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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 ) ∈ L 2 × 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.

How to cite

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Soenjaya, Agus Leonardi. "Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling." Mathematica Bohemica 147.4 (2022): 461-470. <http://eudml.org/doc/298742>.

@article{Soenjaya2022,
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.},
author = {Soenjaya, Agus Leonardi},
journal = {Mathematica Bohemica},
keywords = {low regularity; global well-posedness; Klein-Gordon-Schrödinger equation; higher order coupling},
language = {eng},
number = {4},
pages = {461-470},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling},
url = {http://eudml.org/doc/298742},
volume = {147},
year = {2022},
}

TY - JOUR
AU - Soenjaya, Agus Leonardi
TI - Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling
JO - Mathematica Bohemica
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 147
IS - 4
SP - 461
EP - 470
AB - 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.
LA - eng
KW - low regularity; global well-posedness; Klein-Gordon-Schrödinger equation; higher order coupling
UR - http://eudml.org/doc/298742
ER -

References

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  10. Miao, C., Xu, G., Low regularity global well-posedness for the Klein-Gordon-Schrödinger system with the higher-order Yukawa coupling, Differ. Integral Equ. 20 (2007), 643-656. (2007) Zbl1212.35454MR2319459
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