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

Global existence and decay of solutions to Prandtl system with small analytic data