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Differential invariants for plane flows of viscid fluids

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Abstract

Algebras of symmetries and the corresponding algebras of differential invariants for plane flows of viscid fluids are given. Their dependence on thermodynamical states of media are studied and a classification of thermodynamical states is given.

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References

  1. I. Anderson and C. Torre, The Differential Geometry Package. http://digitalcommons. usu. edu/dg_downloads/4. Accessed 2016.

    Google Scholar 

  2. V. Andreev, O. Kaptsov, V. Pukhnachev, and A. Rodionov, Applications of Group-Theoretical Methods in Hydrodynamics (Springer Science and Business Media, New York, 1998).

    Book  MATH  Google Scholar 

  3. G. Batchelor, An Introduction to Fluid Dynamics (Cambridge Univ. Press, Cambridge, 2000).

    Book  MATH  Google Scholar 

  4. C. Carathéodory, “Untersuchungen über die Grundlagen der Thermodynamik,” Math. Ann. 67, 355–386 (1909).

    Article  MathSciNet  Google Scholar 

  5. A. Duyunova, V. Lychagin, and S. Tychkov, “Differential invariants for plane flows of inviscid fluids,” Anal. Math. Phys. (2017, in press).

    Google Scholar 

  6. B. Kruglikov and V. Lychagin, “Mayer brackets and solvability of PDEs–I,” Differ. Geom. Appl. 17, 251–272 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  7. B. Kruglikov and V. Lychagin, “Global Lie–Tresse theorem,” Selecta Math. 22, 1357–1411 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  8. L. Ovsjannikov, Group Analysis of Differential Equations (Academic, New York, 2014).

    Google Scholar 

  9. M. Rosenlicht, “A remark on quotient spaces,” An. Acad. Brasil 35, 487–489 (1963).

    MathSciNet  MATH  Google Scholar 

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Correspondence to A. Duyunova.

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Submitted by A. M. Elizarov

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Duyunova, A., Lychagin, V. & Tychkov, S. Differential invariants for plane flows of viscid fluids. Lobachevskii J Math 38, 644–652 (2017). https://doi.org/10.1134/S1995080217040084

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  • DOI: https://doi.org/10.1134/S1995080217040084

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