How to stop OSX MySQL filling up error logs
[This question is almost a year old, but anyways I just came across it while investigating the same issue, and although the answer is probably no longer relevant for you, it might be for someone else reading this.]

This can happen when using the standard MySQL installation including the MySQL preference pane. When opening the MySQL preference pane, it will periodically (about once per second) try to connect to localhost, presumably to find out if MySQL is running and display the status accordingly. Interestingly, these connections do not stop when going back to the System Preferences start screen, but they do stop when closing the System Preferences.

When initiating these connections, the preference pane uses various usernames (for whatever reason). On my macOS Sierra with MySQL 5.7.17, I observed _spotlight, _mysql and the current user’s username.

However, if you get those log entries even when System Preferences are closed, this is a different issue in your case.