Invariant tensors and partial differential equations

O. V. Kaptsov

Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences

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.

Keywords: integral invariants, Lie derivative, invariant tensor.

UDC: 517.956

Received: 26.07.2004

 English version: Siberian Mathematical Journal, 2006, 47:2, 258–268

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