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arXiv · 1109.3296

Geometrical dissipation for dynamical systems

Petre Birtea·Dan Comanescu
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Abstract

On a Riemannian manifold $(M,g)$ we consider the $k+1$ functions $F_1,...,F_k,G$ and construct the vector fields that conserve $F_1,...,F_k$ and dissipate $G$ with a prescribed rate. We study the geometry of these vector fields and prove that they are of gradient type on regular leaves corresponding to $F_1,...,F_k$. By using these constructions we show that the cubic Morrison dissipation and the Landau-Lifschitz equation can be formulated in a unitary form.

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Petre Birtea, Dan Comanescu. 2011-09-15. Geometrical dissipation for dynamical systems. https://doi.org/10.1007/s00220-012-1589-6

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