SABINE HITTMEIR, Sara Merino-Aceituno

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In recent works it has been demonstrated that using an appropriate rescaling, linear Boltzmann-type equations give rise to a scalar fractional diffusion equation in the limit of a small mean free path. The equilibrium distributions are typically heavy-tailed distributions, but also classical Gaussian equilibrium distributions allow for this phenomena if combined with a degenerate collision frequency for small velocities. This work aims to an extension in the sense that a linear BGK-type equation conserving not only mass, but also momentum and energy, for both mentioned regimes of equilibrium distributions is considered. In the hydrodynamic limit we obtain a fractional diffusion equation for the temperature and density making use of the Boussinesq relation and we also demonstrate that with the same rescaling fractional diffusion cannot be derived additionally for the momentum. But considering the case of conservation of mass and momentum only, we do obtain the incompressible Stokes equation with fractional diffusion in the hydrodynamic limit for heavy-tailed equilibria.
Original languageEnglish (US)
Pages (from-to)105-129
Number of pages25
JournalKinetic and Related Models
Issue number1
StatePublished - 2016
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2021-11-05
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: SH thanks to the financial support by the Austrian Academy of Sciences OAW via the New Frontiers project NST-0001 and acknowledges the support of the King Abdullah University of Science and Technology (KAUST) within grant KUK-I1-007-43 during the research stay in Cambridge, where this collaboration has been started.; The work of SMA was supported by the UK Engineering and Physical Science Research Council (EPSRC) grant EP/H023348/1 for the University of Cambridge Centre for Doctoral Training, the Cambridge Centre for Analysis; and also by a Fellowship for Graduate Courses funded by the Fundacion Caja Madrid. Finally, SMA thanks to the Wolfang Pauli Institute in Vienna for its hospitality and support during her stays there.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation


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