Global Existence and the Decay of Solutions to the Prandtl System with Small Analytic Data

In this paper, we prove the global existence and large time decay estimate of solutions to Prandtl system with small initial data, which is analytical in tangential variable. The key ingredient used proof derive a sufficiently fast decay-in-time some weighted analytic energy quantity, consists linear combination velocity its primitive one, basically controls evolution radius solutions. Our result can be viewed as global-in-time Cauchy–Kowalevsakya for particular improves previous Ignatova Vicol (Arch Ration Mech Anal 220:809–848, 2016) concerning almost well-posedness two-dimensional system.