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Differential Invariants for Spherical Flows of Inviscid Fluid

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Abstract

Symmetries and the corresponding algebras of differential invariants of inviscid fluids on a sphere are given. Their dependence on thermodynamical states of media is studied, and a classification of thermodynamical states is given.

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References

  1. I. M. Anderson, and C. G. Torre, The Differential Geometry Package. https://doi.org/digitalcommons.usu.edu/dg_downloads/4.

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  6. A. Duyunova, V. Lychagin, and S. Tychkov, “Differential invariants for plane flows of inviscid fluids,”S. Anal. Math. Phys. (2017). doi 10.1007/s13324–017-0169–5

    Google Scholar 

  7. I. Krasilshchik, V. Lychagin, and A. Vinogradov, Geometry of Jet Spaces and Nonlinear Partial Differential Equations (Gordon and Breach Science, 1986).

    Google Scholar 

  8. A. Kushner, V. Lychagin, and V. Rubtsov, Contact Geometry and Nonlinear Differential Equations (Cambridge Univ. Press, Cambridge, 2007).

    MATH  Google Scholar 

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Correspondence to A. A. Duyunova.

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Submitted by M. A. Malakhaltsev

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Duyunova, A.A., Lychagin, V.V. & Tychkov, S.N. Differential Invariants for Spherical Flows of Inviscid Fluid. Lobachevskii J Math 39, 655–663 (2018). https://doi.org/10.1134/S1995080218050062

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  • DOI: https://doi.org/10.1134/S1995080218050062

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