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Invariant tensors and partial differential equations

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Abstract

We consider tensors with coefficients in a commutative differential algebra A. Using the Lie derivative, we introduce the notion of a tensor invariant under a derivation on an ideal of A. Each system of partial differential equations generates an ideal in some differential algebra. This makes it possible to study invariant tensors on such an ideal. As examples we consider the equations of gas dynamics and magnetohydrodynamics.

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Authors and Affiliations

  1. Institute of Computational Modeling, Krasnoyarsk, Russia

    O. V. Kaptsov

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  1. O. V. Kaptsov
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Original Russian Text Copyright © 2006 Kaptsov O. V.

The author was supported by the Russian Foundation for Basic Research (Grant 04-01-00130).

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Translated from Sibirski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Matematicheski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Zhurnal, Vol. 47, No. 2, pp. 316–328, March–April, 2006.

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Kaptsov, O.V. Invariant tensors and partial differential equations. Sib Math J 47, 258–268 (2006). https://doi.org/10.1007/s11202-006-0039-0

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  • DOI: https://doi.org/10.1007/s11202-006-0039-0

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