  We study fluctuations of time-dependent fuzzy two-sphere solutions of the
non-abelian DBI action of D0-branes, describing a bound state of a spherical
D2-brane with N D0-branes. The quadratic action for small fluctuations is shown
to be identical to that obtained from the dual abelian D2-brane DBI action,
using the non-commutative geometry of the fuzzy two-sphere. For some of the
fields, the linearized equations take the form of solvable Lam\'e equations. We
define a large-N DBI-scaling limit, with vanishing string coupling and string
length, and where the gauge theory coupling remains finite. In this limit, the
non-linearities of the DBI action survive in both the classical and the quantum
context, while massive open string modes and closed strings decouple. We
describe a critical radius where strong gauge coupling effects become
important. The size of the bound quantum ground state of multiple D0-branes
makes an intriguing appearance as the radius of the fuzzy sphere, where the
maximal angular momentum quanta become strongly coupled.
