Global Tangentially Analytical Solutions of the 3D Axially Symmetric Prandtl Equations  

作　　者：Xinghong PAN Chaojiang XU 

机构地区：[1]School of Mathematics and Key Laboratory of MIIT,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China [2]School of Mathematics and Key Laboratory of MIIT,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China,and Laboratoire de Mathématiques Raphaël Salem,UMR 6085 CNRSUniversitéde Rouen Normandie,76801 Saint-Étienne-du-Rouvray,France.

出　　处：《Chinese Annals of Mathematics,Series B》2024年第4期573-596,共24页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.12031006,11801268);the Fundamental Research Funds for the Central Universities of China(No.NS2023039)。

摘　　要：In this paper,the authors will prove the global existence of solutions to the three dimensional axially symmetric Prandtl boundary layer equations with small initial data,which lies in H1Sobolev space with respect to the normal variable and is analytical with respect to the tangential variables.The main novelty of this paper relies on careful constructions of a tangentially weighted analytic energy functional and a specially designed good unknown for the reformulated system.The result extends that of Paicu-Zhang in[Paicu,M.and Zhang,P.,Global existence and the decay of solutions to the Prandtl system with small analytic data,Arch.Ration.Mech.Anal.,241(1),2021,403–446].from the two dimensional case to the three dimensional axially symmetric case,but the method used here is a direct energy estimates rather than Fourier analysis techniques applied there.

关 键 词：Global existence Tangentially analytical solutions Axially symmetric Prandtl equations 

分 类 号：O175[理学—数学]