iPhone and iPad
The browser on the iPod touch, iPhone, and iPad is Mobile Safari.
It took several years for Safari to gain support for WebGL.
I checked for how big a web app could be (tried Google
mobile safari offline limit), and it appears to be limited to 5 MB. The localStorage object is likewise limited to 5 MB (tried Google
mobile safari localstorage limit).
Even accelerometer support wasn't added until iOS 4.2.