量子动力学中Klein-Gordon-Schrodinger（KGS）模型被用来描述核子和介子之间的相互作用，在光学、电子学、电动力学、材料以及化学等领域中都有非常重要的应用。由于耦合了不同类型的方程，这类模型的数学研究有很大难度。本项目主要研究KGS型耦合系统在能量空间的适定性和渐近极限，具体包括当非线性指标大于临界Sobolev指数时KGS型系统在能量空间中解的存在性以及整体存在的条件；一般耦合结构下KGS型系统在能量空间中解的唯一性、稳定性以及临界指标；弱初始资料下KGS型系统在能量空间中的非相对论极限等。上述研究不仅对揭示介子在核子场中的运动规律以及介质环境对它的影响有极其重要的理论意义，同时也为能量空间中更广泛意义下量子动力学模型相关属性的研究及方法创新提供支持。

Klein-Gordon-Schrodinger (KGS) model in quantum dynamics is used to describe the interactions between nucleons and mesons, and has very important applications in the field of optics, electronics, electrodynamics, material and chemical etc.. Due to the coupling of equations with different types, the mathematical study of such models is very difficult. This project mainly studies the well posedness and asymptotic limit in energy space for KGS-type system, including the existence of solutions and the conditions for the global existence for KGS system in the energy space when the nonlinear index is greater than the critical Sobolev index; The uniqueness, stability of solution and critical index for KGS system with general coupling structure in the energy space; The nonrelativistic limit in the energy space for KGS system with weak initial data. This study has a very important theoretical significance not only to reveal the movement rules of mesons in the nuclear field and the influnce on the media environment, but also to provide support for the innovation of research methods and the related properties of quantum dynamics model more broadly in the energy space.