In this paper, the authors 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 a 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. The result can be viewed as a global-in-time Cauchy–Kowalevsakya result for the Prandtl system with small analytical data, which in particular improves the previous result in Ignatova and Vicol (Arch RationMech Anal 220:809–848, 2016) concerning the almost global well-posedness of a two-dimensional Prandtl system. 

　　Publication: 

　　-    Archive for Rational Mechanics and Analysis, 241, 1, 403-446 (2021). 

　　Authors: 

　　-    Marius Paicu (Université Bordeaux, France) 

　　-    Ping Zhang (Institute of Mathematics, AMSS, Chinese Academy of Sciences)