Open AccessGlobal solution in a weak energy class for Klein-Gordon-Schrödinger system
Author(s) -
Qinwei Shi,
AUTHOR_ID,
Yaqian Jia,
Xunyang Wang,
AUTHOR_ID
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022033
Subject(s) - sobolev space , klein–gordon equation , singularity , class (philosophy) , schrödinger's cat , dimension (graph theory) , mathematics , mathematical physics , initial value problem , state (computer science) , exponential growth , boundary value problem , space (punctuation) , energy (signal processing) , mathematical analysis , pure mathematics , physics , quantum mechanics , computer science , nonlinear system , statistics , algorithm , artificial intelligence , operating system
Based on the possible singularity of stationary state, we revisit the initial boundary value problem of the classical Klein-Gordon-Schrödinger (KGS) system in one space dimension. The wellposedness is established in a class of Sobolev NLS solutions together with exponentially growing KG solutions.