Statistical solution and Liouville type theorem for the Klein-Gordon-Schrödinger equations

• DOI: 10.1016/j.jde.2021.01.039
• Publication Date: 2021-02-09T20:42:37Z
• Authors: Caidi Zhao; Tomás Caraballo; Grzegorz Łukaszewicz
• Keywords: Pullback attractor; Liouville type theorem; Klein-Gordon-Schdinger equations; 0101 mathematics; Statistical solution; 01 natural sciences; Invariant measure

Agencia Estatal de Investigación (AEI). España PGC2018-096540-B-I00<br/>Fondo Europeo de Desarrollo Regional (FEDER) PGC2018-096540-B-I00<br/>Ministerio de Ciencia e Innovación (MCIU). España PGC2018-096540-B-I00<br/>In this article, the authors investigate the system of Schr odinger and Klein-Gordon equations with Yukawa coupling. They rst prove the existence of pullback attractor and construct a family of invariant Borel probability measures. Then they establish that this family of probability measures satis es a Liouville type theorem and is indeed a statistical solution for the coupling equations. Further, they reveal that the invariant property of the statistical solution is a particular situation of the Liouville type theorem.<br/>