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

作     者：Xinghong PAN Chaojiang XU 

作者机构：School of Mathematics and Key Laboratory of MIIT Nanjing University of Aeronautics and Astronautics Laboratoire de Mathématiques Rapha?l Salem UMR 6085 CNRSUniversité de Rouen Normandie 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊B辑(英文版))

年 卷 期：2024年第45卷第4期

页      面：573-596页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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) 

主　　题：Axially symmetric Global existence Prandtl equations Tangentially analytical solutions 

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 *** 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 *** result extends that of Paicu-Zhang in[Paicu,*** Zhang,P.,Global existence and the decay of solutions to the Prandtl system with small analytic data,***.,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.