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global well-posdness of prandtl system with small analytic data

zhangping yanjiuyuan(zhongkeyuanshuxuesuo)

the key ingredient used in the proof is to derive sufficiently fast decay-in-time estimate of some weighted analytic energy estimate of the tangent velocity, which is based on a poincar\'e type inequality and a subtle interplay between the tangential velocity equation and its primitive one.