Computational Mathematics and Mathematical Physics

, Volume 59, Issue 10, pp 1742–1752 | Cite as

On Smooth Vortex Catastrophe of Uniqueness for Stationary Flows of an Ideal Fluid

  • O. V. TroshkinEmail author


It is well known that the steady-state plane-parallel or spatial axisymmetric flow of an ideal incompressible fluid in a finite-length plane channel or pipe that can be decomposed in powers of spatial coordinates (i.e., is an analytical and, hence, exactly computable flow) is uniquely determined by the inflow vorticity. Under the same boundary conditions, an infinite number of uncomputable phantoms, i.e., infinitely smooth, but nonanalytical flows exist if the domain of a unique analytical flow contains a sufficiently intense vortex cell where the maximum principle is violated for the stream function. A scheme for obtaining an uncomputable vortex phantom for the Euler fluid dynamics equations is described in detail below.


steady-state ideal incompressible fluid plane or axisymmetric finite channel inflow vorticity unique analytical flow violation of the maximum principle nonuniqueness of smooth nonanalytical flows 



This work was performed within the state assignment of the Federal Research Center Scientific Research Institute for System Analysis of the Russian Academy of Sciences (fundamental scientific research, GP 14) on subject no. 0065-2019-0005 “Mathematical Modeling of Dynamic Processes in Deformable and Reacting Media on Multiprocessor Computer Systems,” no. AAAA-A19-119011590092-6.


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Scientific Research Institute for System Analysis, Federal Research Center, Russian Academy of SciencesMoscowRussia

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