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| Global Tangentially Analytical Solutions of the 3D Axially Symmetric Prandtl Equations |
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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 |
| Page view： 1272
Net amount： 447 |
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). |
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| 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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