Mobile Edge Computing Caching System (MECCS) realizes low-latency and high-bandwidth content access and enables seamless 4K Ultra High Definition (UHD) video streaming by caching content in advance at edge-servers of a cellular network. The objective of MECCS is to maximize cache hit by caching highly popular video content while utilizing the storage capacity efficiently in edge-servers. Most of existing caching schemes estimate the popularity of each content based on content request history in off-line or on-line manners, considering the characteristics of Video-on-Demand (VoD) content which has long-term time-varying popularity. However, since live streaming follows Short-term Time-Varying (STV) characteristics, estimating popularity based on content request history do not guarantee acceptable performance on cache hit for live streaming. In this paper, we propose a request model to estimate the popularity distribution considering STV characteristics. Also, we propose a STV request model-based chunk caching scheme to cache highly popular content and enhance cache hit in multiple live channels, utilizing the storage capacity of collaborative edge-servers efficiently. Experimental results show that the proposed scheme outperforms existing schemes regarding cache hit and backhaul traffic.