This is played in the Restaurant of The Ark. 

Improvised song dedicated to the next prime ministers ship

I'm 90% sure this is a piano version of "A Corner of Memories" from Persona 4

The song is called Ark, but when it is played in piano it gives off a sad, depressed vibe. The original is more of a rock

Persona 4 Reincarnation's OST - Like a Dream Come True

Persona 4 OST Reincarnation - Like a Dream Come True

Persona 3 ~ Iwatodai Dorm

I love this song, how about you guys?
:)
You guys can download it!