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Uspekhi Mat. Nauk, 2003, Volume 58, Issue 2(350), Pages 111–122 (Mi umn612)  

This article is cited in 15 scientific papers (total in 15 papers)

On some unresolved issues in non-linear fluid dynamics

K. R. Rajagopal

Texas A&M University

Abstract: This paper is a discussion of some open problems concerning generalizations of Navier–Stokes fluids and other non-linear fluids, which are in need of thorough investigation. The first topic is an interesting generalization of the Navier–Stokes model which is appropriate, in particular, in the description of fluids like water subjected to processes in which the normal stresses are very large. Discussed next is the modelling of non-Newton fluids at a distance from the boundary of the volume occupied by the fluid. Attention is then given to the necessity of a careful revision of conditions obtained at the boundary of the fluid volume, and finally, the modelling of “turbulent” flows is discussed.

DOI: https://doi.org/10.4213/rm612

Full text: PDF file (237 kB)
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English version:
Russian Mathematical Surveys, 2003, 58:2, 319–330

Bibliographic databases:

UDC: 517.9
MSC: Primary 76D05, 76A05, 76F10; Secondary 35Q35, 76D03, 76D10
Received: 15.02.2003

Citation: K. R. Rajagopal, “On some unresolved issues in non-linear fluid dynamics”, Uspekhi Mat. Nauk, 58:2(350) (2003), 111–122; Russian Math. Surveys, 58:2 (2003), 319–330

Citation in format AMSBIB
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\pages 111--122
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\jour Russian Math. Surveys
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\pages 319--330
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. A. Ladyzhenskaya, “Sixth problem of the millennium: Navier–Stokes equations, existence and smoothness”, Russian Math. Surveys, 58:2 (2003), 251–286  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Hoppe R.H.W., Kuzmin M.Y., Litvinov W.G., Zvyagin V.G., “Flow of electrorheological fluid under conditions of slip on the boundary”, Abstr. Appl. Anal., 2006, 43560, 14 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Sohn K., “Airflow velocities in the airways during expiration on different end-expiratory lung volumes: Computational study”, 28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2006, 2725–2728  isi
    4. M. Yu. Kuz'min, “A mathematical model of the motion of a nonlinear viscous fluid with the condition of slip on the boundary”, Russian Math. (Iz. VUZ), 51:5 (2007), 51–60  mathnet  crossref  mathscinet  zmath  elib
    5. A. E. Mamontov, “Globalnaya razreshimost mnogomernykh uravnenii szhimaemoi nenyutonovskoi zhidkosti, transportnoe uravnenie i prostranstva Orlicha”, Sib. elektron. matem. izv., 6 (2009), 120–165  mathnet  mathscinet  elib
    6. Bridges C., Karra S., Rajagopal K.R., “On modeling the response of the synovial fluid: Unsteady flow of a shear-thinning, chemically-reacting fluid mixture”, Computers & Mathematics With Applications, 60:8 (2010), 2333–2349  crossref  mathscinet  zmath  isi
    7. E. S. Baranovskii, “An optimal control problem for a stationary flow of a Jeffreys medium with slip boundary condition”, J. Appl. Industr. Math., 8:2 (2014), 168–176  mathnet  crossref  mathscinet  isi
    8. E. S. Baranovskii, “On steady motion of viscoelastic fluid of Oldroyd type”, Sb. Math., 205:6 (2014), 763–776  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. M. A. Artemov, E. S. Baranovskii, “Granichnye zadachi dlya uravnenii dvizheniya polimernykh zhidkostei c nelineinym usloviem proskalzyvaniya vdol tverdykh stenok”, Tr. IMM UrO RAN, 21, no. 1, 2015, 14–24  mathnet  mathscinet  elib
    10. Baranovskii E.S., “On Flows of Bingham-Type Fluids With Threshold Slippage”, Adv. Math. Phys., 2017, 7548328  crossref  mathscinet  isi
    11. Baranovskii E.S., Artemov M.A., “Steady Flows of Second-Grade Fluids in a Channel”, Vestn. St.-Peterbg. Univ. Ser. 10 Prikl. Mat. Inform. Protsessy, 13:4 (2017), 342–353  crossref  mathscinet  isi
    12. Baranovskii E.S., “Global Solutions For a Model of Polymeric Flows With Wall Slip”, Math. Meth. Appl. Sci., 40:14 (2017), 5035–5043  crossref  mathscinet  zmath  isi
    13. Baranovskii E.S., Artemov M.A., “Steady Flows of Second-Grade Fluids Subject to Stick-Slip Boundary Conditions”, Engineering Mechanics 2017, Engineering Mechanics, Acad Sci Czech Republic, Inst Thermomechanics, 2017, 110–113  isi
    14. Sakhalkar S.V., Bogy D.B., “Effect of Rheology and Slip on Lubricant Deformation and Disk-to-Head Transfer During Heat-Assisted Magnetic Recording (Hamr)”, Tribol. Lett., 66:4 (2018), 145  crossref  isi  scopus
    15. Baranovskii E.S., “Steady Flows of An Oldroyd Fluid With Threshold Slip”, Commun. Pure Appl. Anal, 18:2 (2019), 735–750  crossref  isi  scopus
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