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On the inner turbulence paradigm. (Russian. English summary) Zbl 1413.35374
Summary: In the paper we study the reproducing of the initial phase of the inner turbulence (without regard for the boundary effects). The atypical regularization of multiple-component Euler system is made by the viscosity and diffuse layering introduction. The analogue of Hugoniot condition and the analogue of Lax stability condition are constructed for it. The problem of local accessibility of the phase space points is investigated. The bifurcations of one-front solutions of the abridged Euler system to the two-front solutions are obtained. The supersonic behaviour of bifurcations appearance is shown. The reconstruction of the initial phase of the inner turbulence (without regard for the boundary effects) is made including the mathematical description of the birth of two-speed flow (the Riemann-Hugoniot catastrophe) and alternation.
MSC:
35Q31 Euler equations
35B32 Bifurcations in context of PDEs
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