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

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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 H1 Sobolev 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.

Global existenceTangentially analytical solutionsAxially symmetricPrandtl equations

Xinghong PAN、Chaojiang XU

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School of Mathematics and Key Laboratory of MIIT,Nanjing University of Aeronautics and Astronau-tics,Nanjing 211106,China

Laboratoire de Mathématiques Raphaël Salem,UMR 6085 CNRS-Université de Rouen Normandie,76801 Saint-Étienne-du-Rouvray,France

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaFundamental Research Funds for the Central Universities of China

1203100611801268NS2023039

2024

10.1007/s11401-024-0029-1

数学年刊B辑(英文版)
国家教育部委托复旦大学主办

数学年刊B辑(英文版)

CSTPCD
影响因子：0.129
ISSN：0252-9599
年,卷(期)：2024.45(4)