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

Citation:

Xinghong PAN,Chaojiang XU.Global Tangentially Analytical Solutions of the 3D Axially Symmetric Prandtl Equations[J].Chinese Annals of Mathematics B,2024,45(4):573~596
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Authors:

Xinghong PAN; Chaojiang XU

Foundation:

the National Natural Science Foundation of China (Nos. 12031006, 11801268) and the Fundamental Research Funds for the Central Universities of China (No. NS2023039).
Abstract: 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 H 1 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.

Keywords:

Global existence, Tangentially analytical solutions, Axially symmetric, Prandtl equations

Classification:

35Q35, 76D10
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