Drift diffusion equations with fractional diffusion on compact Lie groups

Duván Cardona; Julio Delgado; Michael Ruzhansky

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arXiv · 2205.02320

Drift diffusion equations with fractional diffusion on compact Lie groups

Duván Cardona·Julio Delgado·Michael Ruzhansky

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Abstract

In this work we investigate the well-posedness for difussion equations associated to subelliptic pseudo-differential operators on compact Lie groups. The diffusion by strongly elliptic operators is considered as a special case and in particular the fractional diffusion with respect to the Laplacian. The general case is studied within the H\"ormander classes associated to a sub-Riemannian structure on the group (encoded by a H\"ormander system of vector fields). Applications to diffusion equations for fractional sub-Laplacians, fractional powers of more general subelliptic operators, and the corresponding quasi-geostrophic model with drift $D$ are investigated. Examples on SU(2) for diffusion problems with fractional diffusion are analysed.

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Duván Cardona, Julio Delgado, Michael Ruzhansky. 2022-05-04. Drift diffusion equations with fractional diffusion on compact Lie groups. https://arxiv.org/abs/2205.02320

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