I am a graduate student just started learning dispersive PDE in MSRI's summer program. I roughly finished reading the paper by Klainerman and Machedon "ON THE UNIQUENESS OF SOLUTIONS TO THE GROSS-PITAEVSKII HIERARCHY". However I do not really know much about the many body system problem in general. May I ask what should I read to understand the general context of their paper and other related topics? I briefly searched on arxiv and found there are quite a few (+30) papers on this topic, but they all seem rather dense. So I do not really know where to start. I am also trying to read Erdos, Schlein, H-T Yau's paper on this topic, but I found myself getting lost after a while as I do not really have enough background. I know basic quantum mechanics and basic PDE, and it seems these are vastly insufficient to understand the huge topic.
I am reading Tao's article (https://terrytao.wordpress.com/2009/11/26/from-bose-einstein-condensates-to-the-nonlinear-schrodinger-equation/#more-3135) and I found it really helpful. However, I am rather lost with questions like "What are the open questions in this topic?" "Why these questions are important?" "Does physicists care about these results?" "What is a meaningful improvement of ths paper?", etc. I also found this phenomenon that we understand the mathematical statement but having poor insight of its physical background (or the real motivation behind the work) is quite common in my study group. So I venture to ask.