On the Well-Posedness for a Class of Pseudo-Differential Parabolic Equations

Delgado, Julio

doi:10.1007/s00020-018-2432-z

Cited by 2 publications

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“…The fractional Laplacian on the torus has been studied in [32] and several aspects of the harmonic analysis of the fractional Laplacian on lattices have been investigated in [8]. Other recent works on the fractional Laplacian and its different generalisations have been considered in [1,[12][13][14][15]17,20,23,30,31,37] and the references therein. In particular, the counterpart of the results proved here for compact Lie groups have been analysed on graded Lie groups in [4] in the case of hypoelliptic problems for Rockland operators.…”

Section: Introductionmentioning

confidence: 99%

Drift diffusion equations with fractional diffusion on compact Lie groups

2022

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In this work we investigate the well-posed for diffusion 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 Hörmander classes associated to a sub-Riemannian structure on the group (encoded by a Hörmander 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 $$\text {SU}(2)$$ SU ( 2 ) for diffusion problems with fractional diffusion are analysed.

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