Two Dimensional Subsonic and Subsonic-Sonic Spiral Flows Outside a Porous Body

In this paper, we investigate two dimensional subsonic and subsonic-sonic spiral flows outside a porous body. The existence and uniqueness of the subsonic spiral flow are obtained via variational formulation, which tends to a given radially symmetric subsonic spiral flow at far field. The optimal de...

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Bibliographic Details
Published in:Acta mathematica scientia 2022-04, Vol.42 (4), p.1569-1584
Main Authors: Weng, Shangkun, Zhang, Zihao
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:In this paper, we investigate two dimensional subsonic and subsonic-sonic spiral flows outside a porous body. The existence and uniqueness of the subsonic spiral flow are obtained via variational formulation, which tends to a given radially symmetric subsonic spiral flow at far field. The optimal decay rate at far field is also derived by Kelvin’s transformation and some elliptic estimates. By extracting spiral subsonic solutions as the approximate sequences, we obtain the spiral subsonic-sonic limit solution by utilizing the compensated compactness. The main ingredients of our analysis are methods of calculus of variations, the theory of second-order quasilinear equations and the compensated compactness framework.
ISSN:0252-9602
1572-9087
DOI:10.1007/s10473-022-0416-1