Open AccessA degenerate elliptic problem from subsonic-sonic flows in convergent nozzles
Author(s) -
Guanming Gai,
Yuanyuan Nie,
Chunpeng Wang
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021070
Subject(s) - degenerate energy levels , mathematical analysis , physics , nozzle , perturbation (astronomy) , boundary (topology) , hölder condition , mathematics , quantum mechanics , thermodynamics
This paper concerns continuous subsonic-sonic potential flows in a two dimensional convergent nozzle, which is governed by a free boundary problem of a quasilinear degenerate elliptic equation. It is shown that for a given nozzle which is a perturbation of an straight one, and a given mass flux, there exists uniquely a continuous subsonic-sonic flow whose velocity vector is along the normal direction at the inlet and the sonic curve. Furthermore, the sonic curve of this flow is a free boundary, where the flow is singular in the sense that the speed is only \begin{document}$ C^{1/2} $\end{document} Hölder continuous and the acceleration blows up at the sonic state.