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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 1999, Volume 40, Issue 2, Pages 24–33 (Mi pmtf3051)  

This article is cited in 35 scientific papers (total in 35 papers)

One class of partially invariant solutions of the Navier–Stokes equations

S. V. Meleshkoa, V. V. Pukhnachevb

a Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, 630090, Novosibirsk
b Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, 630090, Novosibirsk
Abstract: A family of partially invariant solutions of the Navier–Stokes equations of rank 2 and defect 2 is considered. These solutions describe the three-dimensional unsteady motions of a viscous incompressible fluid in which the vertical velocity component and the pressure are independent of the horizontal coordinates. In particular, they can be interpreted as flows in a horizontal layer, one boundary of which is the free surface.
Received: 25.06.1998
English version:
Journal of Applied Mechanics and Technical Physics, 1999, Volume 40, Issue 2, Pages 208–216
DOI: https://doi.org/10.1007/BF02468516
Bibliographic databases:
Document Type: Article
UDC: 532.516
Language: Russian
Citation: S. V. Meleshko, V. V. Pukhnachev, “One class of partially invariant solutions of the Navier–Stokes equations”, Prikl. Mekh. Tekh. Fiz., 40:2 (1999), 24–33; J. Appl. Mech. Tech. Phys., 40:2 (1999), 208–216
Citation in format AMSBIB
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\by S.~V.~Meleshko, V.~V.~Pukhnachev
\paper One class of partially invariant solutions of the Navier--Stokes equations
\jour Prikl. Mekh. Tekh. Fiz.
\yr 1999
\vol 40
\issue 2
\pages 24--33
\mathnet{http://mi.mathnet.ru/pmtf3051}
\elib{https://elibrary.ru/item.asp?id=28814906}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 1999
\vol 40
\issue 2
\pages 208--216
\crossref{https://doi.org/10.1007/BF02468516}
Linking options:
  • https://www.mathnet.ru/eng/pmtf3051
  • https://www.mathnet.ru/eng/pmtf/v40/i2/p24
  • This publication is cited in the following 35 articles:
    1. Gennadii Alekseev, Olga Soboleva, “Inhomogeneous Boundary Value Problems for the Generalized Boussinesq Model of Mass Transfer”, Mathematics, 12:3 (2024), 391  crossref
    2. Evgenii S. Baranovskii, Sergey V. Ershkov, Evgenii Yu. Prosviryakov, Alexander V. Yudin, “Exact Solutions to the Oberbeck–Boussinesq Equations for Describing Three-Dimensional Flows of Micropolar Liquids”, Symmetry, 16:12 (2024), 1669  crossref
    3. A. G. Petrova, V. V. Pukhnachev, O. A. Frolovskaya, “Exact Solutions of Second-Grade Fluid Equations”, Proc. Steklov Inst. Math., 322 (2023), 173–187  mathnet  crossref  crossref
    4. Sergey V. Ershkov, Evgeniy Yu. Prosviryakov, Mikhail A. Artemov, Dmytro D. Leshchenko, “Non-Stationary Helical Flows for Incompressible Couple Stress Fluid”, Mathematics, 11:24 (2023), 4999  crossref
    5. Sergey V. Ershkov, Evgeniy Yu. Prosviryakov, Natalya V. Burmasheva, Victor Christianto, “Solving the Hydrodynamical System of Equations of Inhomogeneous Fluid Flows with Thermal Diffusion: A Review”, Symmetry, 15:10 (2023), 1825  crossref
    6. Sergey Ershkov, Natalya Burmasheva, Dmytro D. Leshchenko, Evgeniy Yu. Prosviryakov, “Exact Solutions of the Oberbeck–Boussinesq Equations for the Description of Shear Thermal Diffusion of Newtonian Fluid Flows”, Symmetry, 15:9 (2023), 1730  crossref
    7. N. V. Burmasheva, E. Yu. Prosviryakov, “Tochnoe reshenie tipa Kuetta – Puazeilya dlya ustanovivshikhsya kontsentratsionnykh techenii”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 164, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2022, 285–301  mathnet  crossref
    8. Sergey V Ershkov, Evgeniy Yu Prosviryakov, Natalya V Burmasheva, Victor Christianto, “Towards understanding the algorithms for solving the Navier–Stokes equations”, Fluid Dyn. Res., 53:4 (2021), 044501  crossref
    9. V. V. Pukhnachev, Nonlinear Physical Science, Symmetries and Applications of Differential Equations, 2021, 251  crossref
    10. V. V. Pukhnachev, E. N. Zhuravleva, “Viscous flows with flat free boundaries”, Eur. Phys. J. Plus, 135:7 (2020)  crossref
    11. Dominik Dierkes, Alexei Cheviakov, Martin Oberlack, “New similarity reductions and exact solutions for helically symmetric viscous flows”, Physics of Fluids, 32:5 (2020)  crossref
    12. V. P. Kovalev, E. Yu. Prosviryakov, “Novyi klass nevintovykh tochnykh reshenii uravnenii Nave–Stoksa”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 224:4 (2020), 762–768  mathnet  crossref  isi
    13. E. N. Zhuravleva, V. V. Pukhnachev, “A Problem on a Viscous Layer Deformation”, Dokl. Phys., 65:2 (2020), 60  crossref
    14. E. Yu. Prosviryakov, “Tochnye resheniya obobschennykh ploskikh techenii Beltrami–Trkala i Bellaba”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 224:2 (2020), 319–330  mathnet  crossref  isi
    15. N P Moshkin, “On Hiemenz flow of Maxwell incompressible viscoelastic medium”, J. Phys.: Conf. Ser., 1268:1 (2019), 012049  crossref
    16. V. Rosenhaus, Ravi Shankar, Cody Squellati, “Semi‐invariant solutions of the Navier‐Stokes equations”, Math Methods in App Sciences, 41:8 (2018), 2853  crossref
    17. Oxana Frolovskaya, Vladislav Pukhnachev, “Analysis of the Models of Motion of Aqueous Solutions of Polymers on the Basis of Their Exact Solutions”, Polymers, 10:6 (2018), 684  crossref
    18. Aleksandr A. Talyshev, AIP Conference Proceedings, 1903, 2017, 030057  crossref
    19. A. D. Polyanin, V. F. Zaitsev, “Transformations, properties, and exact solutions of unsteady axisymmetric boundary layer equations for non-Newtonian fluids”, Theor Found Chem Eng, 51:4 (2017), 437  crossref
    20. S.N. Aristov, V.V. Privalova, E. Y. Prosviryakov, “Stationary nonisothermal Couette flow. Quadratic heating of the upper boundary of the fluid layer”, Nelin. Dinam., 2016, 167  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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