1,998 research outputs found
Estimates of the Green function for the fractional Laplacian perturbed by gradient
The Green function of the fractional Laplacian of the differential order
bigger than one and the Green function of its gradient perturbations are
comparable for bounded smooth multidimensional open sets if the drift function
is in an appropriate Kato class.Comment: 35 pages, details added to the proof of geometrical Lemma
Principal eigenvalue of the fractional Laplacian with a large incompressible drift
We add a divergence-free drift with increasing magnitude to the fractional
Laplacian on a bounded smooth domain, and discuss the behavior of the principal
eigenvalue for the Dirichlet problem. The eigenvalue remains bounded if and
only if the drift has non-trivial first integrals in the domain of the
quadratic form of the fractional Laplacian.Comment: 19 page
Steady state particle distribution of a dilute sedimenting suspension
Sedimentation of a non-Brownian suspension of hard particles is studied. It
is shown that in the low concentration limit a two-particle distribution
function ensuring finite particle correlation length can be found and
explicitly calculated. The sedimentation coefficient is computed. Results are
compared with experiment.Comment: 4 pages, 2 figure
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