Methodological notes

On the problem of boundary conditions for mixed type equations arising in the description of astrophysical transonic flows

  a, b,  a
a Moscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141701, Russian Federation
b Lebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation

Using the example of an exactly solvable problem, it is shown that the number of boundary conditions which is necessary to determine the transonic hydrodynamic flow near the so-called `nonstandard' singular point does not depend on whether the separatrix characteristic passes or does not pass through this point. Thus, a quite popular statement is called into question, according to which the critical surface, on which the regularity condition determines the flow structure, generally coincides with the surface of separatrix characteristics, and not with the sonic surface.

Fulltext pdf (155 KB)
Fulltext is also available at DOI: 10.3367/UFNe.2022.07.039217
Keywords: hydrodynamics
PACS: 95.30.Lz
DOI: 10.3367/UFNe.2022.07.039217
Citation: Beskin V S, Khalilov T I "On the problem of boundary conditions for mixed type equations arising in the description of astrophysical transonic flows" Phys. Usp. 66 741–746 (2023)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 2nd, February 2022, revised: 4th, July 2022, 8th, July 2022

Оригинал: Бескин В С, Халилов Т И «К проблеме граничных условий для уравнений смешанного типа, возникающих при описании астрофизических трансзвуковых течений» УФН 193 791–797 (2023); DOI: 10.3367/UFNr.2022.07.039217

References (38) Similar articles (9) ↓

  1. A.M. Fridman, O.V. Khoruzhii “Nonuniversality of the classical concept of the tangential discontinuity36 (3) 171–176 (1993)
  2. A.G. Bershadskii “Large-scale fractal structure in laboratory turbulence, astrophysics, and the ocean33 (12) 1073–1075 (1990)
  3. E.A. Andryushin, V.L. Ginzburg, A.P. Silin “Boundary conditions in the macroscopic theory of superconductivity36 (9) 854–857 (1993)
  4. V.S. Beskin, V.I. Par’ev “Axially symmetric steady-state flows in the vicinity of a Kerr black hole and the nature of the activity of galactic nuclei36 (6) 529–539 (1993)
  5. V.S. Beskin, A.A. Zheltoukhov “On the anomalous torque applied to a rotating magnetized sphere in a vacuum57 799–806 (2014)
  6. A.P. Vinogradov “On the form of constitutive equations in electrodynamics45 331–338 (2002)
  7. V.E. Antonov “A rule for a joint of three boundary lines in phase diagrams56 395–400 (2013)
  8. A.L. Zuev, K.G. Kostarev “Certain peculiarities of the solutocapillary convection51 1027–1045 (2008)
  9. V.I. Klyatskin “Statistical description of the diffusion of a passive tracer in a random velocity field37 501–513 (1994)

The list is formed automatically.

© 1918–2023 Uspekhi Fizicheskikh Nauk
Email: Editorial office contacts About the journal Terms and conditions