So, you built an application by yourself, with no funding or help,and you're willing to give up 50% of the equity just like that?

I'd also recommend seeing a lawyer. Additionally, a partnership may not be the best idea if you don't know and trust this second co-founder. I'm no lawyer, but it sounds like an LLC might be a better choice. You can vest his shares over a time period that you feel is appropriate, and include a clause in the operating agreement that discharges him if he fails to perform the duties required of him.

Again, I'd go see a lawyer. It's not worth the headache later on.