Scale up as you grow — whether you're running one virtual machine or ten thousand.

From GPU-powered inference and Kubernetes to managed databases and storage, get everything you need to build, scale, and deploy intelligent applications.

This textbox defaults to using Markdown to format your answer.
You can type !ref in this text area to quickly search our full set of tutorials, documentation & marketplace offerings and insert the link!
These answers are provided by our Community. If you find them useful, show some love by clicking the heart. If you run into issues leave a comment, or add your own answer to help others.
Go with the lines that say ERROR.
170117 17:39:35 InnoDB: Fatal error: cannot allocate memory for the buffer pool
Your droplet needs more memory or you need to make MySQL use less of it.
This comment has been deleted
It does appear that you’re running out of memory from the details provided. In order to prevent these issues, you should upgrade your droplet. MySQL and forks, such as MariaDB, can be ran on 512MB droplets, but it’s a balancing act and you’d need to be comfortable working from the CLI in order to work on optimizing your configurations.
You can reduce the amount of RAM required by MySQL (or MariaDB) in order to work with less RAM, but what works for a little while may not work long-term. It’s also a trade off. Working with less RAM often means that MySQL won’t perform as well as it should and would with more RAM free.
Looking beyond MySQL, WordPress can sometimes be resource intensive, so it’s important to enable some sort of caching, especially on resource-constrained servers. W3TC and WP Super Cache are two that instantly come to mind when it comes to caching. They will allow you to use PHP’s built-in object caching (if OPCode Caching is enabled), though that too takes RAM (as would Memcached or Redis).
The benefit to enabling caching, however, is that you an reduce the resources required by your web server as a result since instead of constantly performing dynamic operations normally required by WordPress, the caching serves statically generated pages until the cache is updated.