Using a Dynamic IP

I have been using OwnCloud for a long time and love it!

I just had my Hard drive fail. I have backup so I am fine with that.
I was thing about making a portable OwnCloud server.
Before I replace the hard drive I was wondering about rebuilding the OwnCloud using Wi-Fi on a public network.( i.e. Starbucks, McDonalds, etc )
I was wondering if I had a Dynamic IP could OwnCloud still be used?
Most of what I have read, shows OC go to a URL or a static IP.

Can I use a dynamic IP or would it be better to just stay with my Static IP.

I am using the latest update on OwnCloud on a Ubuntu server.