eZ Publish uses the Monolog component to log errors, and it has a RotatingFileHandler that allows for file rotation. According to their documentation, it "logs records to a file and creates one logfile per day. It will also delete files older than $maxFiles". But then, their own recommendation is to use "logrotate" instead of doing the rotation in the handler as you would have better performance. More details here:

https://github.com/Seldaek/monolog
http://linuxcommand.org/man_pages/logrotate8.html

If it is decided to use monolog's handler, it can be configured in /ezpublish/config/config.yml.

Example:

monolog:
    handlers:
        main:
            type: rotating_file
            max_files: 10
            path: "%kernel.logs_dir%/%kernel.environment%.log"
            level: debug