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Analysis and application of ellipticity of stability equations on fluid mechanics. (English) Zbl 1145.76381
Summary: 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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##### References:
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