  In this paper, we prove the global existence and the large time decay
estimate of solutions to Prandtl system with small initial data, which is
analytical in the tangential variable. The key ingredient used in the proof is
to derive sufficiently fast decay-in-time estimate of some weighted analytic
energy estimate to a quantity, which consists of a linear combination of the
tangential velocity with its primitive one, and which basically controls the
evolution of the analytical radius to the solutions. Our result can be viewed
as a global-in-time Cauchy-Kowalevsakya result for Prandtl system with small
analytical data.
