Analysis and application of ellipticity of stability equations on fluid mechanics.

*(English)*Zbl 1145.76381Summary: By using characteristic analysis of the linear and nonlinear parabolic stability equations (PSE), PSE of primitive disturbance variables are proved to be parabolic in total. By using sub-characteristic analysis of PSE, the linear PSE are proved to be elliptical and hyperbolic-parabolic for velocity \(U\) in subsonic and supersonic, respectively; the nonlinear PSE are proved to be elliptical and hyperbolic-parabolic for velocity \(U+u\) in subsonic and supersonic, respectively. Methods are gained that remove the remaining ellipticity from the PSE by characteristic and sub-characteristic theories, the results for the linear PSE are consistent with the known results, and the influence of the Mach number is also given out. At the same time, the methods of removing the remained ellipticity are further obtained from the nonlinear PSE.

##### MSC:

76E30 | Nonlinear effects in hydrodynamic stability |

35Q35 | PDEs in connection with fluid mechanics |

35K55 | Nonlinear parabolic equations |

35K65 | Degenerate parabolic equations |

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\textit{M. Li} and \textit{Z. Gao}, Appl. Math. Mech., Engl. Ed. 24, No. 11, 1334--1341 (2003; Zbl 1145.76381)

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